Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Given an nn matrix Aandn1 column matrices B,C,andX, solve AX+C=B for X. Assume that all necessary inverses exist.Use matrix inverse methods to solve the system: 3x1x2+x3=1x1+x2=3x1+x3=2 [Note: The Inverse of the coefficient matrix was found in Matched Problem 2, Section 4.5]Use matrix inverse methods to solve each of the following systems (see Matched Problem 2): A3x1x2+x3=3x1+x2=3x1+x3=2 B3x1x2+x3=5x1+x2=1x1+x3=4Repeat Example 4 with investment A paying 4 and investment B paying 12.In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 5x=3In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 4x=9In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 4x=8x+7In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 6x=3x+14In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 6x+8=2x+17In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 4x+3=5x+12In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 103x=7x+9In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section 1.1 ). 2x+7x+1=8x+3xWrite Problems 9-12 as systems of linear equations without matrices. 3121x1x2=54Write Problems 9-12 as systems of linear equations without matrices. 2134x1x2=57Write Problems 9-12 as systems of linear equations without matrices. 310201132x1x2x3=342Write Problems 9-12 as systems of linear equations without matrices. 210231403x1x2x3=647Write each system in Problems 13-16 as a matrix equation of the form AX=B. 3x14x2=12x1+x2=5Write each system in Problems 13-16 as a matrix equation of the form AX=B. 2x1+x2=85x1+3x2=4Write each system in Problems 13-16 as a matrix equation of the form AX=B. x1x2+2x3=32x1+3x2=1x1+x2+4x3=2Write each system in Problems 13-16 as a matrix equation of the form AX=B. 3x12x3=9x1+4x2+x3=72x1+3x2=6Find x1andx2 in problems 17-20. x1x2=321421Find x1andx2 in problems 17-20. x1x2=211232Find x1andx2 in problems 17-20. x1x2=232132Find x1andx2 in problems 17-20. x1x2=310221In Problems 21-24, find x1 and x2. 1112x1x2=57In Problems 21-24, find x1 and x2. 1314x1x2=96In Problems 21-24, find x1 and x2. 1123x1x2=1510In Problems 21-24, find x1 and x2. 1132x1x2=1020In Problems 25-30, solve for x1andx2. 1311x1x2+52=147In Problems 25-30, solve for x1andx2. 2113x1x2+35=1016In Problems 25-30, solve for x1andx2. 26412x1x2+52=147In Problems 25-30, solve for x1andx2. 2163x1x2+35=1016In Problems 25-30, solve for x1andx2. 4231x1x243=148In Problems 25-30, solve for x1andx2. 3221x1x241=43In Problems 31-38, write each system as a matrix equation and solve using inverses. x1+2x2=k1x1+3x2=k2 (A) k1=1,k2=3 (B) k1=3,k2=5 (C) k1=2,k2=1In Problems 31-38, write each system as a matrix equation and solve using inverses. 2x1+x2=k15x1+3x2=k2 (A) k1=2,k2=13 (B) k1=2,k2=4 (C) k1=1,k2=3In Problems 31-38, write each system as a matrix equation and solve using inverses. x1+3x2=k12x1+7x2=k2 (A) k1=2,k2=1 (B) k1=1,k2=0 (C) k1=3,k2=1In Problems 31-38, write each system as a matrix equation and solve using inverses. 2x1+x2=k1x1+x2=k2 (A) k1=1,k2 (B) k1=2,k2 (C) k1=2,k2In Problems 31-38, write each system as a matrix equation and solve using inverses. x13x2=k1x2+x3=k22x1x2+4x3=k3 (A) k1=1,k2=0,k3= (B) k1=1,k2=1,k3=0 (C) k1=2,k2=2,k3=1In Problems 31-38, write each system as a matrix equation and solve using inverses. 2x1+3x2=k1x1+2x2+3x3=k2x25x3=k3 (A) k1=0,k2=2,k3=1 (B) k1=2,k2=0,k3=1 (C) k1=3,k2=1,k3=0In Problems 31-38, write each system as a matrix equation and solve using inverses. x1+x2=k12x1+3x2x3=k2x1+2x3=k3 (A) k1=2,k2=0,k3=4 (B) k1=0,k2=4,k3=2 (C) k1=4,k2=2,k3=0In Problems 31-38, write each system as a matrix equation and solve using inverses. x1x3=k12x1x2=k2x1+x22x3=k3 (A) k1=4,k2=8,k3=0 (B) k1=4,k2=0,k3=4 (C) k1=0,k2=8,k3=8In Problems 39-44, the matrix equation is not solved correctly. Explain the mistake and find the correct solution. Assume that the indicated inverses exist. AX=B,X=BAIn Problems 39-44, the matrix equation is not solved correctly. Explain the mistake and find the correct solution. Assume that the indicated inverses exist. XA=B,X=BAIn Problems 39-44, the matrix equation is not solved correctly. Explain the mistake and find the correct solution. Assume that the indicated inverses exist. XA=B,X=A1BIn Problems 39-44, the matrix equation is not solved correctly. Explain the mistake and find the correct solution. Assume that the indicated inverses exist. AX=B,X=BA1In Problems 39-44, the matrix equation is not solved correctly. Explain the mistake and find the correct solution. Assume that the indicated inverses exist. AX=BA,X=A1BA,X=BIn Problems 39-44, the matrix equation is not solved correctly. Explain the mistake and find the correct solution. Assume that the indicated inverses exist. XA=AB,X=ABA1,X=BIn Problems 45-50, explain why the system cannot the solved by matrix inverse methods. Discuss methods that could be used and then solve the system. 2x1+4x2=56x112x2=15In Problems 45-50, explain why the system cannot the solved by matrix inverse methods. Discuss methods that could be used and then solve the system. 2x1+4x2=56x112x2=15In Problems 45-50, explain why the system cannot the solved by matrix inverse methods. Discuss methods that could be used and then solve the system. x13x22x3=12x1+6x+24x3=3In Problems 45-50, explain why the system cannot the solved by matrix inverse methods. Discuss methods that could be used and then solve the system. x13x22x3=12x1+7x+23x3=3In Problems 45-50, explain why the system cannot the solved by matrix inverse methods. Discuss methods that could be used and then solve the system. x12x2+3x3=12x13x22x3=3x1x25x3=2In Problems 45-50, explain why the system cannot the solved by matrix inverse methods. Discuss methods that could be used and then solve the system. x12x2+3x3=12x13x22x3=3x1x25x3=4For nn matrices A and B, and n1 column matrices C,DandX. Solve each matrix equation in Problems 51-56 for X. Assume that all necessary inverses exist. AXBX=CFor nn matrices A and B, and n1 column matrices C,DandX. Solve each matrix equation in Problems 51-56 for X. Assume that all necessary inverses exist. AX+BX=CFor nn matrices A and B, and n1 column matrices C,DandX. Solve each matrix equation in Problems 51-56 for X. Assume that all necessary inverses exist. AX+X=CFor nn matrices A and B, and n1 column matrices C,DandX. Solve each matrix equation in Problems 51-56 for X. Assume that all necessary inverses exist. AXX=CFor nn matrices A and B, and n1 column matrices C,DandX. Solve each matrix equation in Problems 51-56 for X. Assume that all necessary inverses exist. AXC=DBXFor nn matrices A and B, and n1 column matrices C,DandX. Solve each matrix equation in Problems 51-56 for X. Assume that all necessary inverses exist. AX+C=BX+DIn Problems 57 and 58, solve for x1andx2. 51047x1x22133x1x2=9735In Problems 57 and 58, solve for x1andx2. 5122x1x23213x1x2=2031In Problems 59-62. Write each system as a matrix equation and solve using the inverse coefficient matrix. Use a graphing calculator or computer to perform the necessary calculations. x1+5x2+6x3=762x1+3x2+8x3=9211x1+9x2+4x3=181In Problems 59-62. Write each system as a matrix equation and solve using the inverse coefficient matrix. Use a graphing calculator or computer to perform the necessary calculations. 7x1+2x2+7x3=592x1+x2+x3=153x1+4x2+9x3=53In Problems 59-62. Write each system as a matrix equation and solve using the inverse coefficient matrix. Use a graphing calculator or computer to perform the necessary calculations. 2x1+x2+5x3+5x4=373x14x2+3x3+2x4=07x1+3x2+8x3+4x4=455x1+9x2+6x3+7x4=94In Problems 59-62. Write each system as a matrix equation and solve using the inverse coefficient matrix. Use a graphing calculator or computer to perform the necessary calculations. 2x1+x2+6x3+5x4=543x14x2+15x3+2x4=847x1+3x2+7x3+4x4=345x1+9x2+7x3+7x4=77Construct a mathematical model for each of the following problems. (The answers in the back of the book include both the mathematical model and the interpretation of its solution.) Use matrix inverse methods to solve the model and then interpret the solution. Concert tickets. A concert hall has 10,000 scats and two categories of ticket prices, 25 and 35. Assume that all seats in each category can be sold. (A) How many tickets of each category should be sold to bring in each of the returns indicated in the table? (B) Is it possible to bring in a return of 200,000 ? Of 400,000 ? Explain. (C) Describe all the possible returns.Construct a mathematical model for each of the following problems. (The answers in the back of the book include both the mathematical model and the interpretation of its solution.) Use matrix inverse methods to solve the model and then interpret the solution. Parking receipts. Parking fees at a zoo are 5.00 for local residents and 7.50 for all others. At the end of each day, the total number of vehicles parked that day and the gross receipts for the day are recorded, but the number of vehicles in each category is not. The following table contains the relevant information for a recent 4-day period: (A) How many vehicles in each category' used the zoo’s parking facilities each day? (B) If 1,200 vehicles are parked in one day, is it possible take in gross receipts of 5,000 5,000? Of 10,000 ? Explain. (C) Describe all possible gross receipts on a day when 1,200 vehicles are parked.Construct a mathematical model for each of the following problems. (The answers in the back of the book include both the mathematical model and the interpretation of its solution.) Use matrix inverse methods to solve the model and then interpret the solution. Production scheduling. A supplier manufactures car and truck frames at two different plants. The production rates ( in frames per hour) for each plant are given in the table: How many hours should each plant be scheduled to operate to exactly fill each of the orders in the following table?Construct a mathematical model for each of the following problems. (The answers in the back of the book include both the mathematical model and the interpretation of its solution.) Use matrix inverse methods to solve the model and then interpret the solution. Production scheduling. Labor and material costs for manufacturing two guitar models are given in the table: (A) If a total of 3,000 a week is allowed for labor and material, how many of each model should be produced each week to use exactly each of the allocations of the 3,000 indicated in the following table? (B) Is it possible to use an allocation of 1,600 for labor and 1,400 for material? Of 2,000 for labor and 1,000 for material? Explain.Incentive plan. A small company provides an incentive plan for its top executives. Each executive receives as a bonus a percentage of the portion of the annual profit that remains after the bonuses for the other executives have been deducted (see the table). If the company has an annual profit of 2 million, find the bonus for each executive. Round each bonus to the nearest hundred dollars.Incentive plan. Repeat Problem 67 if the company decides to include a 1 bonus for the sales manager in the incentive plan.Diets. A biologist has available two commercial food mixes containing the percentage of protein and fat given in the table. (A) How many ounces of each mix should be used to prepare each of the diets listed in the following table? (B) Is it possible to prepare a diet consisting of 100 ounces of protein and 22 ounces of fat? Of 80 ounces of protein and 15 ounces of fat? Explain.Education. A stale university system is planning to hire new faculty at the rank of lecturer or instructor for several of its two-year community colleges. The number of sections taught and the annual salary (in thousands of dollars) for each rank are given in the table. The number of sections taught by new faculty and the amount budgeted for salaries (in thousands of dollars) at each of the colleges arc given in the following table. How many faculty of each rank should be hired at each college to exactly meet the demand for sections and completely exhaust the salary budget?If equations 2 and 3 are valid for an economy with n industries, discuss the size of all the matrices in each equation. The next example illustrates the application of equations 2 and 3 to a three-industry economy.An economy is based on three sectors, coal, oil and transportation. Production of a dollar's worth of coal requires an input of 0.20 from the coal sector and 0.40 from the transportation sector. Production of a dollar’s worth of oil requires an input of 0.10 from the oil sector and 0.20 from the transportation sector. Production of a dollar’s worth of transportation requires an input of 0.40 from the coal sector, 0.20 from the oil sector, and 0.20 from the transportation sector. (A) Find the technology matrix M. (B) Find 1M1 (C) Find the output from each sector that is needed to satisfy a final demand of 30 billion for coal, 10 billion for oil and 20 billion for transportation.In Problems 18, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=3x+6In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=4x5In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=0.9x+10In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=0.6x+84In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=0.2x+3.2In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l.l.) x=0.3x+4.2In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=0.68x+2.56In Problems 1-8, solve each equation for x, where x represents a real number. (If necessary, review Section l .l.) x=0.98x+8.24Problems 9-14 pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture A and energy E. The technology matrix M and final demand matrices (in billions of dollars) are AEAE0.40.20.20.1=M D1=64D2=85D3=129 How much input from A and E are required to produce a dollar's worth of output for A ?Problems 9-14 pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture A and energy E. The technology matrix M and final demand matrices (in billions of dollars) are AEAE0.40.20.20.1=M D1=64D2=85D3=129 How much input from A and E are required to produce a dollar’s worth of output for E ?Problems 9-14 pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture A and energy E. The technology matrix M and final demand matrices (in billions of dollars) are AEAE0.40.20.20.1=M D1=64D2=85D3=129 Find IMandIM1.Problems 9-14 pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture A and energy E. The technology matrix M and final demand matrices (in billions of dollars) are AEAE0.40.20.20.1=M D1=64D2=85D3=129 Find the output for each sector that is needed to satisfy the final demand D1.Problems 9-14 pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture A and energy E. The technology matrix M and final demand matrices (in billions of dollars) are AEAE0.40.20.20.1=M D1=64D2=85D3=129 Repeat Problem 12 for D2 .Problems 9-14 pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture A and energy E. The technology matrix M and final demand matrices (in billions of dollars) are AEAE0.40.20.20.1=M D1=64D2=85D3=129 Repeat Problem 12 for D3.Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture A, building B. and energy E.The technology matrix M and final demand matrices (in billions of dollars) are ABEABE0.30.20.20.10.10.10.20.10.1=M D1=51015D2=201510 How much input from A,B , and E are required to produce a dollar's worth of output for A ?Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture A, building B. and energy E.The technology matrix M and final demand matrices (in billions of dollars) are ABEABE0.30.20.20.10.10.10.20.10.1=M D1=51015D2=201510 How much of each of A ’s output dollars is required as input for each of the three sectors?Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture A, building B. and energy E.The technology matrix M and final demand matrices (in billions of dollars) are ABEABE0.30.20.20.10.10.10.20.10.1=M D1=51015D2=201510 Find IM.Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture A, building B. and energy E.The technology matrix M and final demand matrices (in billions of dollars) are ABEABE0.30.20.20.10.10.10.20.10.1=M D1=51015D2=201510 Find IM1. Show that IM1IM=I.Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture A, building B. and energy E.The technology matrix M and final demand matrices (in billions of dollars) are ABEABE0.30.20.20.10.10.10.20.10.1=M D1=51015D2=201510 Use IM1 in Problem 18 to find the output for each sector that is needed to satisfy the final demand D1.Problems 15-20 pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture A, building B. and energy E.The technology matrix M and final demand matrices (in billions of dollars) are ABEABE0.30.20.20.10.10.10.20.10.1=M D1=51015D2=201510 Repeat Problem 19 for D2.In Problems 21-26, find IM1 and X. M=0.20.20.30.3;D=1025In Problems 21-26, find IM1 and X. M=0.40.20.60.8;D=3050In Problems 21-26, find IM1 and X. M=0.70.80.30.2;D=2575In Problems 21-26, find IM1 and X. M=0.40.10.20.3;D=1520In Problems 21-26, find IM1 and X. M=0.30.10.30.20.10.20.10.10.1;D=20510In Problems 21-26, find IM1 and X. M=0.30.20.30.10.10.10.10.20.1;D=102515The technology matrix for an economy based on agriculture A and manufacturing M is AMM=AM0.30.250.10.25 (A) Find the output for each sector that is needed to satisfy a final demand of 40 million for agriculture and 40 million for manufacturing. (B) Discuss the effect on the final demand if the agriculture output in part (A) is increased by 20 million and manufacturing output remains unchanged.The technology matrix for an economy based on energy E and transportation T is ETM=ET0.250.250.40.2 (A) Find the output for each sector that is needed to satisfy a final demand of $50 million for energy and $50 million for transportation. (B) Discuss the effect on the final demand if the transportation output in part (A) is increased by $40 million and the energy output remains unchanged.Refer to Problem 27. Fill in the elements in the following technology matrix. MAT=MA0.30.250.10.25 Use this matrix to solve Problem 27. Discuss any differences in your calculations and in your answers.Refer lo Problem 28. Fill in the elements in the following technology matrix. ETT=TE0.250.250.40.2 Use this matrix to solve Problem 28. Discuss any differences in your calculations and in your answers.The technology matrix for an economy based on energy E and mining M is EMM=EM0.20.30.40.3 The management of these two sectors would like to set the total output level so that the final demand is always 40 of the total output. Discuss methods that could be used to accomplish this objective.The technology matrix for an economy based on automobiles A and construction C is ACM=AC0.10.40.10.1 The management of these two sectors would like to set the total output level so that the final demand is always 70 of the total output. Discuss methods that could be used to accomplish this objective.All the technology matrices in the text have elements between 0 and 1.Why is this the case? Would you ever expect to find an element in a technology matrix that is negative? That is equal to 0 ? That is equal to 1 ? That is greater than 1 ?The sum of the elements in a column of any of the technology matrices in the text is less than 1 why is this the case? Would you ever expect to find a column with a sum equal to 1 ? Greater than 1 ? How would you describe an economic system where the sum of the elements in every column of the technology matrix is 1?Coal, steel. An economy is based on two industrial sectors, coal and steel. Production of a dollar's worth of coal requires an input of 0.10 from the coal sector and 0.20 from the steel sector. Production of a dollar's worth of steel requires an input of 0.20 from the coal sector and 0.40 from the steel sector. Find the output for each sector that is needed to satisfy a final demand of 20 billion for coal and 10 billion for steel.Transportation, manufacturing. An economy is based on two sectors, transportation and manufacturing. Production of a dollar's worth of transportation requires an input of 0.10 from each sector and production of a dollar's worth of manufacturing requires an input of 0.40 from each sector. Find the output for each sector that is needed to satisfy a final demand of 5 billion for transportation and 20 billion for manufacturing.Agriculture, tourism. The economy of a small island nation is based on two sectors, agriculture and tourism. Production of a dollar's worth of agriculture requires an input of 0.20 from agriculture and 0.15 from tourism. Production of a dollar’s worth of tourism requires an input of 0.40 from agriculture and 0.30 from tourism. Find the output from each sector that is needed to satisfy a final demand of 60 million for agriculture and 80 million for tourism.Agriculture, oil. The economy of a country is based on two sectors, agriculture and oil. Production of a dollar's worth of agriculture requires an input of 0.40 from agriculture and 0.35 from oil. Production of a dollar's worth of oil requires an input of 0.20 from agriculture and 0.05 from oil. Find the output from each sector that is needed to satisfy a final demand of 40 million for agriculture and 250 million for oil.Agriculture, manufacturing, energy. An economy is based on three sectors, agriculture, manufacturing, and energy. Production of a dollar's worth of agriculture requires inputs of 0.20 from agriculture, 0.20 from manufacturing, and 0.20 from energy. Production of a dollar’s worth of manufacturing requires inputs of 0.40 from agriculture 0.10 from manufacturing, and 0.10 from energy. Production of a dollar's worth of energy requires inputs of 0.30 from agriculture, 0.10 from manufacturing, and 0.10 from energy. Find the output for each sector that is needed to satisfy a final demand of 10 billion for agriculture. 15 billion for manufacturing, and 20 billion for energy.Electricity, natural gas, oil. A large energy company produces electricity, natural gas and oil. The production of a dollar's worth of electricity requires inputs of 0.30 from electricity 0.10 from natural gas, and 0.20 from oil. Production of a dollar's worth of natural gas requires inputs of 0.30 from electricity, 0.10 from natural gas and 0.20 from oil. Production of a dollar’s worth of oil requires inputs of 0.10 from each sector. Find the output for each sector that is needed to satisfy a final demand of 25 billion for electricity, 15 billion for natural gas, and 20 billion for oil.Four sectors. An economy is based on four sectors, agriculture A, energy E, labor L. and manufacturing M.The table gives the input requirements for a dollar's worth of (in billions of dollars) for a 3 -year period. Find the output from each sector that is needed to satisfy a final de- for each sector that is needed to satisfy each of these final demands. Round answers to the nearest billion dollars.Repeal Problem 41 with the following tableSolve the following system by graphing 2xy=4x2y=4Solve the system in Problem 1 by substitution 2xy=4x2y=4If a matrix is in reduced form, say so. If not, explain why and state the row operation(s) necessary to transform the matrix into reduced form. A011023B100323C10101123D11001123Given matrices A and B. A=5310248130 B=320417 (A) What is the size of A?OfB? (B) Find a24,a15,b31,andb22. (C) Is AB defined? Is BA defined?Find x1andx2 : (A) 1213x1x2=42 (B) 5311x1x2+2514=1822In Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 A+BIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 B+DIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 A2BIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 ABIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 ACIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 ADIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 DCIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 CDIn Problem 6-14, perform the operations that are defined, given the following matrices: A=1231B=2111C=23D=12 C+DFind the inverse of the matrix A given below by appropriate row operations on AI. Show that A1A=I. A=4332Solve the following system using elimination by addition: 4x1+3x2=33x1+2x2=5Solve the system in Problem 16 by performing appropriate row operations on the augmented matrix of the system. 4x1+3x2=33x1+2x2=5Solve the system in Problem 16 by writing the system as a matrix equation and using the inverse of the coefficient matrix (see Problem 15 ). Also, solve the system if the constants 3 and 5 are replaced by 7 and 10 respectively. By 4 and 2, respectively.In Problems 19-24, perform the operations that are defined, given the following matrices: A=221032B=123C=213D=321112E=3410 A+DIn Problems 19-24, perform the operations that are defined, given the following matrices: A=221032B=123C=213D=321112E=3410 E+DAIn Problems 19-24, perform the operations that are defined, given the following matrices: A=221032B=123C=213D=321112E=3410 DA3EIn Problems 1924, perform the operations that are defined, given the following matrices: A=221032B=123C=213D=321112E=3410 BCIn Problems 19-24, perform the operations that are defined, given the following matrices: A=221032B=123C=213D=321112E=3410 CBIn Problems 19-24, perform the operations that are defined, given the following matrices: A=221032B=123C=213D=321112E=3410 ADBCFind the inverse of the matrix A given below by appropriate row operations on AI. Show that A1A=I. A=123234121Solve by Gauss-Jordan elimination: (A) x1+2x2+3x3=12x1+3x2+4x3=3x1+2x2+x3=3 (B) x1+2x2x3=22x1+3x2+x3=33x1+5x2=1 (C) x1+x2+x3=83x1+2x2+4x3=21Solve the system in Problem 26A by writing the system as a matrix equation and using the inverse of the coefficient matrix (see Problem 25 ). Also, solve the system if the constants 1, 3, and 3 are replaced by 0,0,and2, respectively. By 3,4,and1, respectively.Discuss the relationship between the numbers of solutions of the following system and the constant k. 2x16x2=4x1+kx2=2An economy is based on two sectors, agriculture and energy. Given the technology matrix M and the final demand matrix D (in billions of dollars), find IM1 and the output matrix X : AEM=AE0.20.150.40.3D=AE3020Use the matrix M in Problem 29 to fill in the elements in the following technology matrix. EAT=EA Use this matrix to solve Problem 29. Discuss any differences in your calculations and in your answers.An economy is based on two sectors, coal and steel. Given the technology matrix M and the final demand matrix D (in billions of dollars), find IM1 and the output matrix X : CSM=CS0.450.650.550.35D=CS4010Use graphical approximation techniques on a graphing calculator to find the solution of the following system to two decimal places: x5y=52x+3y=12Find the inverse of the matrix A given below. Show that A1A=I. A=456454111Solve the system 0.04x1+0.05x2+0.06x3=3600.04x1+0.05x20.04x3=120x1+x2+x3=7,000 by writing it as a matrix equation and using the inverse of the coefficient matrix. (Before starting, multiply the first two equations by 100 to eliminate decimals. Also, see Problem 33.)Solve Problem 34 by Gauss-Jordan elimination.Given the technology matrix M and the final demand matrix D (in billions of dollars), find IM1 and the output matrix X : M=0.200.40.10.30.100.40.2D=402030Discuss the number of solutions for a system of n equations in n variables if the coefficient matrix (A) Has an inverse. (B) Does not have an inverseDiscuss the number of solutions for the system corresponding to the reduced form shown below if (A) m0 (B) m=0andn0 (C) m=0andn=0 10201300m53nOne solution to the input-output equation X=MX+D is given by X=IM1D Discuss the validity of each step in the following solutions of this equation. (Assume that all necessary inverses exist.) Are both solutions correct? AX=MX+DXMX=DXIM=DX=DIM1 BX=MX+DD=MXXD=MIXX=MI1DBreak-even analysis. A cookware manufacturer is preparing to market a new pasta machine. The company’s fixed costs for research, development, tooling,etc., are $243,000 and the variable costs are $22.45 per machine. The company sells the pasta machine for $59.95. (A) Find the cost and revenue equations. (B) Find the break-even point. (C) Graph both equations in the same coordinate system and show the break-even point. Use the graph to determine the production levels that will result in a profit and in a loss.Resource allocation. An international mining company has two mines in Voisey’ s Bay and Hawk Ridge. The composition of the ore from each field is given in the table. How many tons of ore from each mine should be used to obtain exactly 6 tons of nickel and 8 tons of copper?Resource allocation. (A) Set up Problem 41 as a matrix equation and solve using the inverse of the coefficient matrix. (B) Solve Problem 41 as in part A if 7.5 tons of nickel and 7 tons of copper are needed.Business leases. A grain company wants to lease a fleet of 20 covered hopper railcars with a combined capacity of 108,000 cubic feet. Hoppers with three different carrying capacities are available: 3,000 cubic feet. 4,500 cubic feet, and 6,000 cubic feet. (A) How many of each type of hopper should they lease? (B) The monthly rates for leasing these hoppers are $180 for 3,000 cubic feet, $225 for 4,500 cubic feet, and $325 for 6,000 cubic feet. Which of the solutions in part (A) would minimize the monthly leasing costs?Material costs. A manufacturer wishes to make two different bronze alloys in a metal foundry. The quantities of copper, tin and zinc needed are indicated in matrix M.The costs for these materials (in dollars per pound) from two suppliers are summarized in matrix N. The company must choose one supplier or the other. CooperTinZincM=4.800lb600lb300lb6,000lb1.400lb700lbAlloy1Alloy2 SupplierASupplierBN=$0.75$0.70$6.50$6.70$0.40$0.50CopperTinZinc (A) Discuss possible interpretations of the elements in the matrix products MNandNM. (B) If either product MNorNM has a meaningful interpretation, find the product and label its rows and columns. (C) Discuss methods of matrix multiplication that can be used to determine the supplier that will provide the necessary materials at the lowest cost.Labor costs. A company with manufacturing plants in California and Texas has labor-hour and wage requirements for the manufacture of two inexpensive calculators as given in matrices M and N below: LabourhourspercalculatorFabricatingdepartmentAssemblydepartmentPackagingdepartmentM=0.15hr0.10hr0.05hr0.25hr0.20hr0.05hrModelAModelB HourlyWagesCaliforniaplantTexasplantN=1210151276FabricatingdepartmentAssemblydepartmentPackagingdepartment (A) Find the labor cost for producing one model B calculator at the California plant. (B) Discuss possible interpretations of the elements in the matrix products MN and NM. (C) If either product MN or NM has a meaningful interpretation, find the product and label its rows and columns.Investment analysis. A person has $5,000 to invest, part at 5 and the rest at 10. How much should be invested at each rate to yield $400 per year? Solve using augmented matrix methods.Investment analysis. Solve Problem 46 by using a matrix equation and the inverse of the coefficient matrix.Investment analysis. In Problem 46, is it possible to have an annual yield of $200?Of$600? Describe all possible annual yields.Ticket prices. An outdoor amphitheater has 25,000 seats. Ticket prices are 8,12,and20, and the number of tickets priced at 8 must equal the number priced at 20. How many tickets of each type should be sold (assuming that all seats can be sold) to bring in each of the returns indicated in the table? Solve using the inverse of the coefficient matrix.Ticket prices. Discuss the effect on the solutions to Problem 49 if it is no longer required to have an equal number of $8 tickets and $20 tickets.Input-output analysis. An economy is based on two industrial sectors, agriculture and fabrication. Production of a dollar’s worth of agriculture requires an input of 0.30 from the agriculture sector and 0.20 from the fabrication sector. Production of a dollar’s worth of fabrication requires 0.10 from the agriculture sector and 0.40 from the fabrication sector. (A) Find the output for each sector that is needed to satisfy a final demand of 50 billion for agriculture and 20 billion for fabrication. (B) Find the output for each sector that is needed to satisfy a final demand of 80 billion for agriculture and 60 billion for fabrication.Cryptography. The following message was encoded with the matrix B shown below. Decode the message. 72530196242082851414923281562113114212629 B=110101111Traffic flow. The rush-hour traffic flow (in vehicles per hour) for a network of four one-way streets is shown in the figure. (A) Write the system of equations determined by the flow of traffic through the four intersections. (B) Find the solution of the system in part (A). (C) What is the maximum number of vehicles per hour that can travel from Oak Street to Elm Street on 1st Street? What is the minimum number? (D) If traffic lights are adjusted so that 500 vehicles per hour travel from Oak Street to Elm Street on 1st Street, determine the flow around the rest of the network.In Step 2 of Example 1, 0,0 was used as a test point in graphing a linear inequality. Describe those linear inequalities for which 0,0 is not a valid test point. In that case, how would you choose a test point to make calculation easy?Graph 6x3y18.Graph (A) y4 (B) 4x9 (C) 3x2yFind the linear inequality whose graph is given in Figure 14. Write the boundary line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.A food vendor at a rock concert sells hot dogs for $4 and hamburgers for $5. How many of these sandwiches must be sold to produce sales of at least $1,000 ? Express the answer as a linear inequality and draw its graph.For Problems 1-8, if necessary, review Section 1.2. Is the point 3,5 on the line y=2x+1 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 7,9 on the line y=3x11 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 3,5 in the solution set of y2x+1 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 7,9 in the solution set of y3x11 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 10,12 on the line 13x11y=2 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 21,25 on the line 30x27y=1 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 10,12 in the solution set of 13x11y2 ?For Problems 1-8, if necessary, review Section 1.2. Is the point 21,25 in the solution set of 30x27y1 ?Graph each inequality in Problems 9-18. yx1Graph each inequality in Problems 9-18. yx+1Graph each inequality in Problems 9-18. 3x2y6Graph each inequality in Problems 9-18. 2x5y10Graph each inequality in Problems 9-18. x4Graph each inequality in Problems 9-18. y5Graph each inequality in Problems 9-18. 6x+4y24Graph each inequality in Problems 9-18. 4x+8y32Graph each inequality in Problems 9-18. 5x2yGraph each inequality in Problems 9-18. 6x4yIn Problems 19-22, (A) graph the set of points that satisfy the inequality. (B) graph the set of points that do not satisfy the inequality. 2x+3y18In Problems 19-22, (A) graph the set of points that satisfy the inequality. (B) graph the set of points that do not satisfy the inequality. 3x+4y24In Problems 19-22, (A) graph the set of points that satisfy the inequality. (B) graph the set of points that do not satisfy the inequality. 5x2y20In Problems 19-22, (A) graph the set of points that satisfy the inequality. (B) graph the set of points that do not satisfy the inequality. 3x5y30In Problems 23-32, define the variable and translate the sentence into an inequality. There are fewer than 10 applicants.In Problems 23-32, define the variable and translate the sentence into an inequality. She consumes no more than 900 calories per day.In Problems 23-32, define the variable and translate the sentence into an inequality. He practices no less than 2.5 hours per day.In Problems 23-32, define the variable and translate the sentence into an inequality. The average attendance is less than 15,000.In Problems 23-32, define the variable and translate the sentence into an inequality. The monthly take-home pay is over $3,000.In Problems 23-32, define the variable and translate the sentence into an inequality. The discount is at least 5%.In Problems 23-32, define the variable and translate the sentence into an inequality. The tax rate is under 40%.In Problems 23-32, define the variable and translate the sentence into an inequality. The population is greater than 500,000.\ In Problems 23-32, define the variable and translate the sentence into an inequality. The enrollment is at most 30.In Problems 23-32, define the variable and translate the sentence into an inequality. Mileage exceeds 35 miles per gallon.In Exercises 33-38, state the linear inequality whose graph is given in the figure. Write the boundary-line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.In Exercises 33-38, state the linear inequality whose graph is given in the figure. Write the boundary-line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.In Exercises 33-38, state the linear inequality whose graph is given in the figure. Write the boundary-line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.In Exercises 33-38, state the linear inequality whose graph is given in the figure. Write the boundary-line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.In Exercises 33-38, state the linear inequality whose graph is given in the figure. Write the boundary-line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.In Exercises 33-38, state the linear inequality whose graph is given in the figure. Write the boundary-line equation in the form Ax+By=C, where A,BandC are integers, before stating the inequality.In Problems 39-44, define two variables and translate the sentence into an inequality. Enrollment in finite mathematics plus enrollment in calculus is less than 300.In Problems 39-44, define two variables and translate the sentence into an inequality. New-car sales and used-car sales combined are at most $500,000.In Problems 39-44, define two variables and translate the sentence into an inequality. Revenue is at least $20,000 under the cost.In Problems 39-44, define two variables and translate the sentence into an inequality. The Democratic candidate beat the Republican by at least seven percentage points.In Problems 39-44, define two variables and translate the sentence into an inequality. The number of grams of saturated fat is more than three times the number of grams of unsaturated fat.In Problems 39-44, define two variables and translate the sentence into an inequality. The plane is at least 500 miles closer to Chicago than to Denver.In Problems 45-54, graph each inequality subject to the non-negative restrictions. 25x+40y3,000,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 24x+30y7,200,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 15x50y1,500,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 16x12y4,800,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 18x+30y2,700,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 14x+22y1,540,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 40x55y0,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 35x+75y0,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 25x+75y600,x0,y0In Problems 45-54, graph each inequality subject to the non-negative restrictions. 75x+25y600,x0,y0In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Seed costs. Seed costs for a farmer are $90 per acre for corn and $70 per acre for soybeans. How many acres of each crop should the farmer plant if he wants to spend no more than $11,000 on seed?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Labor costs. Labor costs for a farmer are $120 per acre for corn and $100 per acre for soybeans. How many acres of each crop should the farmer plant if he wants to spend no more than $15,000 on labor?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Fertilizer. A farmer wants to use two brands of fertilizer for his corn crop. Brand A contains 26%nitrogen,3%phosphate,and3%potash. Brand B contains 16%nitrogen,8%phosphate,and8%potash. (Source: Spectrum Analytic, Inc.) (A) How many pounds of each brand of fertilizer should he add to each acre if he wants to add at least 120 pounds of nitrogen to each acre? (B) How many pounds of each brand of fertilizer should be add to each acre if he wants to add at most 28 pounds of phosphate to each acre?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Fertilizer. A farmer wants to use two brands of fertilizer for his soyabean crop. Brand A contains 18%nitrogen,24%phosphate,and12%potash. Brand B contains 5%nitrogen,10%phosphate,and15%potash. (Source: Spectrum Analytic, Inc.) (A) How many pounds of each brand of fertilizer should he add to each acre if he wants to add at least 50 pounds of phosphate to each acre? (B) How many pounds of each brand of fertilizer should be add to each acre if he wants to add at most 60 pounds of potash to each acre?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Textiles. A textile mill uses two blended yarns-a standard blend that is 30%acrylic,30%wool,and40%nylon and a deluxe blend that is 9%acrylic,39%wool,and52%nylon -to produce various fabrics. How many pounds of each yarn should the mill use to produce a fabric that is at least 20%acrylic ?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Textiles. Refer to Exercise 59. How many pounds of each yarn should the mill use to produce a fabric that is at least 45%nylon ?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Customized vehicles. A company uses sedans and minivans to produce custom vehicles for transporting hotel guests to and from airports. Plant A can produce 10sedansand8minivans per week, and Plant B can produce 8sedansand6minivans per week. How many weeks should each plant operate in order to produce at least 400sedans ?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Customized vehicles. Refer to Exercise 61. How many weeks should each plant operate in order to produce at least 480minivans ?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Political advertising. A candidate has budgeted $10,000 to spend on radio and television advertising. A radio ad costs $200per30-secondspot, and a television ad costs $800per30-secondspot. How many radio and television spots can the candidate purchase without exceeding the budget?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Political advertising. Refer to Problem 63. The candidate decides to replace the television ads with newspaper ad that costs $500 per ad. How many radio spots and newspaper ads can the candidate purchase without exceeding the budget?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Mattresses. A company produces foam mattresses in two sizes: regular and king. It takes 5 minutes to cut the foam for a regular mattress and 6 minutes for a king mattress. If the cutting department has 50 labor-hours available each day, how many regular and king mattresses can be cut in one day?In Problems 55-66, express your answer as a linear inequality with appropriate nonnegative restrictions and draw its graph. Mattresses. Refer to Problem 65. It takes 15 minutes to cover a regular mattress and 20 minutes to cover a king mattress. If the covering department has 160 labor-hours available each day, how many regular and king mattresses can be covered in one day?Determine whether the solution region of each system of linear inequalities is bounded or unbounded. Ay1Bx100Cxyx0y200yxy0x0x0y0y0Solve the following system of linear inequalities graphically: 3x+y21x2y0Solve the following system of linear inequalities graphically and find the corner points: 5x+y20x+y12x+3y18x0y0A manufacturing plant makes two types of inflatable boats––a two person boat and a four-person boat. Each two-person boat requires 0.9 labor-hour in the cutting department and 0.8 labor-hour in the assembly department. Each four-person boat requires 1.8 labor-hours in the cutting department and 1.2 labor-hours in the assembly department. The maximum labor-hours available each month in the cutting and assembly departments are 864 and 672, respectively. (A) Summarize this information in a table. (B) If x two-person boats and y four-person boats are manufactured each month, write a system of linear inequalities that reflects the conditions indicated. Graph the feasible region.For Problems 1-8, if necessary, review Section 1.2. Problems 1-4 refer to the following system of linear inequalities: 4x+y203x+5y37x0y0 Is the point 3,5 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 1-4 refer to the following system of linear inequalities: 4x+y203x+5y37x0y0 Is the point 4,5 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 1-4 refer to the following system of linear inequalities: 4x+y203x+5y37x0y0 Is the point 3,6 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 1-4 refer to the following system of linear inequalities: 4x+y203x+5y37x0y0 Is the point 2,6 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 5-8 refer to the following system of linear inequalities: 5x+y327x+4y45x0y0 Is the point 4,3 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 5-8 refer to the following system of linear inequalities: 5x+y327x+4y45x0y0 Is the point 5,3 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 5-8 refer to the following system of linear inequalities: 5x+y327x+4y45x0y0 Is the point 6,2 in the solution region?For Problems 1-8, if necessary, review Section 1.2. Problems 5-8 refer to the following system of linear inequalities: 5x+y327x+4y45x0y0 Is the point 5,2 in the solution region?In Problems 9-12, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. x+2y83x2y0In Problems 9-12, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. x+2y83x2y0In Problems 9-12, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. x+2y83x2y0In Problems 9-12, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. x+2y83x2y0In Problems 13-16, solve each system of linear inequalities graphically. 3x+y6x4In Problems 13-16, solve each system of linear inequalities graphically. 3x+4y12y3In Problems 13-16, solve each system of linear inequalities graphically. x2y122x+y4In Problems 13-16, solve each system of linear inequalities graphically. 2x+5y20x5y5In Problems 17-20, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. Identify the corner points of each solution region. x+3y182x+y16x0y0In Problems 17-20, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. Identify the corner points of each solution region. x+3y182x+y16x0y0In Problems 17-20, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. Identify the corner points of each solution region. x+3y182x+y16x0y0In Problems 17-20, match the solution region of each system of linear inequalities with one of the four regions shown in the figure. Identify the corner points of each solution region. x+3y182x+y16x0y0In Problems 21-28, is the solution region bounded or unbounded? 3x+y6x0y0In Problems 21-28, is the solution region bounded or unbounded? x+2y4x0y0In Problems 21-28, is the solution region bounded or unbounded? 5x2y10x0y0In Problems 21-28, is the solution region bounded or unbounded? 4x3y12x0y0In Problems 21-28, is the solution region bounded or unbounded? x+y4x10x0y0In Problems 21-28, is the solution region bounded or unbounded? xy3x9x0y0In Problems 21-28, is the solution region bounded or unbounded? x+2y22xy2x0y0In Problems 21-28, is the solution region bounded or unbounded? x+2y22xy2x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+3y12x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 3x+4y24x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+y10x+2y8x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 6x+3y243x+6y30x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+y10x+2y8x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 4x+3y243x+4y8x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+y10x+y7x+2y12x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 3x+y21x+y9x+3y21x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+y16x+y12x+2y14x0y0Solve the systems in Problems 29-38 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 3x+y24x+y16x+3y30x0y0Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. x+4y323x+y304x+5y51Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. x+y11x+5y152x+y12Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 4x+3y482x+y24x9\ Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+3y24x+3y15y4Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. xy02xy40x8Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+3y12x+3y30y5Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. x+3y15xy9x+y9x5Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. x+y105x+3y152x+3y152x5y6Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 16x+13y1203x+4y254x+3y11Solve the systems in Problems 39-48 graphically and indicate whether each solution region is bounded or unbounded. Find the coordinates of each corner point. 2x+2y2110x+5y243x+5y37Problems 49 and 50 introduce an algebraic process for finding the corner points of a solution region without drawing a graph. We will discuss this process later in this chapter. Consider the following system of inequalities and corresponding boundary lines: 3x+4y363x+4y=363x+2y303x+2y=30x0x=0y0y=0 (A) Use algebraic methods to find the intersection points (if any exist) for each possible pair of boundary lines. (There are six different possible pairs) (B) Test each intersection point in all four inequalities to determine which are corner points.Problems 49 and 50 introduce an algebraic process for finding the corner points of a solution region without drawing a graph. We will discuss this process later in this chapter. Consider the following system of inequalities and corresponding boundary lines: 2x+y162x+y=162x+3y362x+3y=36x0x=0y0y=0 (A) Use algebraic methods to find the intersection points (if any exist) for each possible pair of boundary lines. (There are six different possible pairs) (B) Test each intersection point in all four inequalities to determine which are corner points.Water skis. A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The trick ski requires 6 labor-hours for fabricating and 1 labor-hours for finishing. The slalom ski requires 4 labor-hours for fabricating and 1 labor-hours for finishing. The maximum labor-hours available per day for fabricating and finishing are 108 and 24, respectively. If x is the number of trick skis and y is the number of slalom skis produced per day, write a system of linear inequalities that indicates appropriate restraints on x and y. Find the set of feasible solutions graphically for the number of each type of ski that can be produced.Furniture. A furniture manufacturing company manufactures dining-room tables and chairs. A table requires 8 labor-hours for assembling and 2 labor-hours for finishing. A chair requires 2 labor-hours for assembling and 1 labor-hour for finishing. The maximum labor-hours available per day for assembly and finishing are 400 and 120, respectively. If x is the number of tables and y is the number of chairs produced per day, write system of linear inequalities that indicates appropriate restraints on x and y. Find the set of feasible solutions graphically for the number of tables and chairs that can be produced.Water skis. Refer to Problem 51. The company makes a profit of $50 on each trick ski and a profit of $60 on each slalom ski. (A) If the company makes 10 trick skis and 10 slalom skis per day, the daily profit will be $1,100. Are there other production schedules that will result in a daily profit of 1,100 ? How are these schedules related to the graph of the line 50x+60y=1,100 ? (B) Find a production schedule that will produce daily profit greater than $1,100 and repeat part (A) for this schedule. (C) Discuss methods for using lines like those in parts (A) and (B) to find the largest possible daily profit.Furniture. Refer to Problem 52. The company makes a profit of $50 on each table and a profit of $15 on each chair. (A) If the company makes 20 tables and 20 chairs per day, the daily profit will be $1,300. Are there other production schedules that will result in a daily profit of $1,300 ? How are these schedules related to the graph of the line 50x+15y=1,300 ? (B) Find a production schedule that will produce a daily profit greater than $1,300 and repeat part (A) for this schedule. (C) Discuss methods for using lines like those in parts (A) and (B) to find the largest possible daily profit.