1. The table shows the numbers of hours require in each of three departments to make a unit of variousproducts named A, B, and C. For example, product B required 1 hour of time in Department I, 3 hoursin Department Il and 7 hours in Department III.Hours Required Per Unit of ProductDepartmentAC11II137II713Find the numbers of units of A, B and C that could be made if Department I has 75 hours available, DepartmentIl has 85 hours available and Department III has 175 hours available.

Answered: Image /qna-images/answer/c326c129-c4a1-4aa7-b72b-aa187c16de8a.jpg

Answered: 1. The table shows the numbers of hours…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...

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Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.
Suppose we have a supply of 6000 units of S and 8000 units of T, where S and T are used materials in the manufacture of certain products P, Q and R. If each unit of P demands 2 units of S and 0 units of T, each unit of Q uses 3 units of S and 4 units of T, and each unit of R uses 1 unit of S and 4 of T. How many units of P, Q and R must occur if the entire supply is to be consumed?
A company makes two products (X and Y) using two machines (A and B). Each unit of X that is produced requires 50 minutes of processing time on machine A and 30 minutes of processing time on machine B. Each unit of Y that is produced requires 24 minutes of processing time on machine A and 33 minutes of processing time on machine B. At the start of the current week, there are 30 units of X and 90 units of Y in stock. Available processing time on machine A is forecast to be 40 hours and on the machine, B is forecast to be 35 hours. The demand for X in the current week is forecast to be 75 units and for Y is forecast to be 95 units. Company policy is to maximize the combined sum of the units of X and the units of Y in stock at the end of the week. Formulate the problem of deciding how much of each product to make in the current week as a linear program. Solve this linear program using excel.
A producer has three products, A, B, and C, which are composed from many of the same raw materials and subassemblies by the same skilled workforce. Each unit of product A uses 15 units of raw material X, a single purge system subassembly, a case, a power cord, three labor hours in the assembly department, and one labor hour in the finishing department. Each unit of product B uses 10 units of raw material X, five units of raw material Y, two purge system subassemblies, a case, a power cord, five labor hours in the assembly department, and 90 minutes in the finishing department. Each unit of product C uses five units of raw material X, 25 units of raw material Y, two purge system subassemblies, a case, a power cord, seven labor hours in the assembly department, and three labor hours in the finishing department. Labor between the assembly and finishing departments is not transferable, but workers within each department work on any of the three products. There are three full-time (40…
Suppose a maquiladora with two types of parts as raw material: type A and type B. In a first stage of assembly using A and Bs the weapon types are produced two M and N. In a second stage of assembly using the types M and N the types of reinforcements X and Y are produced. knows that to assemble 4 Xs and 3 Ys, a total of 38 Ms and 20 Ns and that to assemble 4 Xs and 1 Ys were required in total 26 Ms and 12 Ns. Furthermore, it is known that to obtain an M requires 4 As and 4 Bs and for an N requires 1 As and 2 Bs. Indicate, in order, how many A and B pieces required to build an X and how many to build a Y. Determine: A) the system of linear equations that models the previous context. B) the solution of the system using some SEL solution method seen in class (example: Gaussian elimination; Gauss-Jordan; Cramer's rule, etc.). C) Respond to the problem raised.
Consider two small companies, each with 9 employees including 1 boss with the highest salary in each company, and 8 people working for them with lower salaries. The table below gives the annual salaries of the people in each company. These salaries are identical except for the fact that Small Company B is more profitable overall, and their boss decides to keep a much higher salary than the boss of Small Company A. Small Company A Small Company B $85 000 (boss A) $360 000 (boss B) $65 000 $65 000 $60 000 $60 000 $40 000 $40 000 $35 000 $35 000 $35 000 $35 000 $35 000 $35 000 $30 000 $30 000 $30 000 $30 000 For each of the two companies, calculate the mean, median, and mode, and show your answers and calculations in the space below (rounded to the nearest thousands place). After you answer this question, answer the two follow-up questions about the results you just calculated.
A chemical company produces three products, A, B, and C, and can sell these products in unlimited quantities at the following unit prices: A, $10; B, $55 C, $100. Producing a unit of A requires one hour of labor, a unit of B, two hours of labor plus two units of A; and a unit of C three hours of labor plus one unit of B. Any A that is used to produce B cannot be sold. Similarly, any B that is used to produce C cannot be sold. A total of 4000 hours of labor is available. Only as many as 500 units of product C can be sold Determine how to maximize the companys revenue.
A dietician wishes to plan a meal around three foods, The percentages of the daily requirements of proteins, carbohydrates and iron contained in each ounce of the three foods are summarized un the following table food 1 food 2 food three protein % 10 6 8 carbohydrates % 10 12 6 iron % 5 4 12 The dietician desires each meal to meet exactly the daily requirement of protein, carbohydrates and iron (100%) of each. 1. Using the information in the table above, write a system of three equations. 2. Write the system in matrix form Ax=b' 3. Using the inverse method, determine how many ounces of each food should the dietician include in the meal to meet the daily requirements exactly?
Suppose a primitive economy consists of two industries, farm products and farm machinery.Suppose that to make one unit of products 0.6 units of products and 0.2 units of machinery arerequired as inputs. Similarly, to make one unit of machinery 0.2 units of products and 0.4 units ofmachinery are required as inputs. If surpluses of 81 units of farm products and 5 units of farmmachinery are desired, find the gross production of each industry.
Parent W requires one of component B and two of component C. Both B and Care run on work center 10. Setup time for B is 2 hours, and run time is 0.1 hour perpiece. For component C, setup time is 2 hours, and run time is 0.15 hour per piece. Ifthe rated capacity of the work center is 80 hours, how many Ws should be producedin a week?
question 2 Hiring workers A company payshis skilled workers S15 per hour in his departmentassembly tool. semi-skilled workersin that department they earn S9 per hour To the employeestwo of shipments are paid SIO per hour Because of aincrease in orders, the company needs to contractemploy a total of 70 workers in the departments ofassembly and shipping Will pay a total of $760 per hourto these employees. Because of a contract with the unionlaw, twice as many semi-semi-workers should be employed.lified than skilled workers. How manysemi-skilled workers, skilled workers and employees ofshipments should hire the company? Note: Solve by Inverse-Excel # OF SEMI-SKILLED WORKERS # OF SKILLED WORKERS # OF SHIPPING WORKERS

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