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A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GHC10, GHC12, and GHC12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company's resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufa cturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit. a) Formulate a linear programming model for this problem. The model was solved using solver and part of the results is provided in the table below. Use it to answer the questions that follow. Variable Cells

A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GHC10, GHC12, and GHC12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company's resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufa cturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit. a) Formulate a linear programming model for this problem. The model was solved using solver and part of the results is provided in the table below. Use it to answer the questions that follow. Variable Cells

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 49P
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Linear programming company-1

A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GHC10, GHC12, and GHC12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company's resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufa cturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit. a) Formulate a linear programming model for this problem. The model was solved using solver and part of the results is provided in the table below. Use it to answer the questions that follow. Variable Cells Redu Objectiv Allowabl Allowabl Final се e e e Valu Coeffici Decreas Cell Name e Cost ent Increase e $B$ 10 X1 = 4 10 6 4 $B$ 2.66666 11 X2 = 4 12 6667 4 %3D $B$ 2.66666 12 X3 = 4 12 6667 4 %3D Constraints Shad Constrai Allowabl Allowabl Final ow nt e e Valu R.H. Decreas Cell Name e Price Side Increase e $F$ Manufacturin 6.66666 g Usage $F$ Assembly Usage $F$ Testing 20 3.6 20 6667 10 6.66666 6. 20 1.6 20 6667 10 6.66666 Usage b) Determine the the optimal solution to the problem. 7 20 1.6 20 6667 10 c) Which resource constraint(s) are binding? Give a reason. d) If the company could increase manufacturing hours by 10 hours per week or increase the assembly hours by 10 per week, which should it choose? Advise the MD, providing detailed explanation using your answer.
Transcribed Image Text:A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GHC10, GHC12, and GHC12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company's resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufa cturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit. a) Formulate a linear programming model for this problem. The model was solved using solver and part of the results is provided in the table below. Use it to answer the questions that follow. Variable Cells Redu Objectiv Allowabl Allowabl Final се e e e Valu Coeffici Decreas Cell Name e Cost ent Increase e $B$ 10 X1 = 4 10 6 4 $B$ 2.66666 11 X2 = 4 12 6667 4 %3D $B$ 2.66666 12 X3 = 4 12 6667 4 %3D Constraints Shad Constrai Allowabl Allowabl Final ow nt e e Valu R.H. Decreas Cell Name e Price Side Increase e $F$ Manufacturin 6.66666 g Usage $F$ Assembly Usage $F$ Testing 20 3.6 20 6667 10 6.66666 6. 20 1.6 20 6667 10 6.66666 Usage b) Determine the the optimal solution to the problem. 7 20 1.6 20 6667 10 c) Which resource constraint(s) are binding? Give a reason. d) If the company could increase manufacturing hours by 10 hours per week or increase the assembly hours by 10 per week, which should it choose? Advise the MD, providing detailed explanation using your answer.
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
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