Modeling Alternatives using Linear Programming for production

Question

Maxine’s Hat Company produces three distinct hat styles.  The operations manager has modeled the operations using linear programming.   He is using x1, x2, x3 to represent each hat style. Below is his formulation:

Maximize Z = 70 x1 + 80 x2 + 60 x3

Subject to:

Machine A:     2 x1 + 4 x2 + 2 x3  < 120 hours

Machine B:     5 x1 + 3 x2 + 2 x3  < 400 hours

Machine C:     2 x1 + 2 x2 + 4 x3  < 110 hours

x1  > 0;   x2  > 0;   x3  > 0

a. Use Excel and Solver to find the optimal solution for this problem.  Provide printouts of worksheets for the final solution and the sensitivity report.  Then consider the statements below independently, state whether they are true or false and explain each answer.

b. If the price of Hat 3 were to be increased by $55, it would be part of the optimal product mix.

c. The capacity of Machine B can be reduce to 280 hours without affecting profits.

d. If  machine  C  had  a  capacity  of  115  hours,  the  production  output  would  remain unchanged.

Summary

The question belongs to Operations Management and it is about using linear programming for modeling three alternatives for production with machine A, machine B and machine C. The calculations have been given in the excel sheet attached along with the question.

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