The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X1 X2 S2 S3 1 1. 0. 12 3 1 1 27 1 1 - 3 - 2 1 |when X2 =, s, =, s2 =, and s3 =: %3D %3D The maximum is X1 %3D %3D (Type integers or simplified fractions.) N O O or
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- You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).A market analyst working for a small appliance manufacturer finds that if the firm produces and sells x blenders annually, a model for the total profit (in dollars) is P(x) = 8x + 0.3x2 − 0.001x3 − 372. Graph the function P in an appropriate viewing rectangle, and use the graph to answer the following questions. (a) When just a few blenders are manufactured, the firm loses money (profit is negative). (For example, P(10) = −263, so the firm loses $263.00 if it produces and sells only 10 blenders.) How many blenders must the firm produce to break even? (Round your answer to the nearest whole number.) blenders(b) Does profit increase indefinitely as more blenders are produced and sold? YesNo If not, what is the largest possible profit the firm could have? (If profit increases indefinitely, enter your answer as ∞. Otherwise, round your answer to the nearest cent.)INCORRECT FORFormulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. (Let BR = pounds of Brazilian beans purchased to produce Regular, BD = pounds of Brazilian beans purchased to produce DeCaf, CR = pounds of Colombian beans purchased to produce Regular, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max 2.033BR+2.582BD+1.868CR+2.418CD INCORRECT Pounds of Regular BR+CR≤900 INCORRECT Pounds of DeCaf BD+CD≤400 INCORRECT
- For the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3DConsider the given LP:Maximize z = 4x1 + 6x2 + 8x3Subject to 3x1 + 2x2 + 5x3<= 30 9x1 + 2x2 + 7x3 <= 126 2x1 + 3x2 + x3<= 60 xi>= 01-Find the optimal values of Z, x1, x2, x3 by using the simplex method.3-If the RHS of the constraint 1 is 34 instead of 30, what is the new value of Z?Which of the following is the optimal value of the objective function for the LP model in this problem? Minimize z=4x + 8y Subject to: x+1.6y>=45 2x+0.5y>=40 X+y<=40 XY>=0 a.220 b.160 c.240 d.200