Question 1 A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GH₵10, GH₵12, and GH₵12 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 manufacturing, 2 hours in assembly, and 1 hour in testing. The Company 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. b) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. c) Advice the management about objective function value corresponding to your answer in (b).
Question 1
A company produces 3 products. Each unit of product 1, 2, and 3 generate a
profit of GH₵10, GH₵12, and GH₵12 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 manufacturing, 2 hours in assembly, and 1 hour in testing. The
Company 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.
b) Management have asked you to determine the optimal solution. Write
your answer in a form of a report to be submitted to the management.
c) Advice the management about objective function value corresponding to
your answer in (b).
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