Question

MSA Computer Corporation manufactures two models of minicomputers, the Alpha 4 and the Beta 5. The firm employs six technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor hours to assemble each Alpha 4 computer and 25 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each.

1.   Determine the most profitable number of each model of minicomputer to produce during the coming month.

2.   What would the profit be if they decided to make at least 15 of each model?

hint : This is quantitative Analysis of management subject

Answer 1

This is an LP problem.

The decision variables are to produce X number of Alpha 4 and Y number of Beta 5.

The X and Y should be produced in such a way to maximize profit. This means the objective function is

Maximize P = 1200X + 1800Y

The constraints are

20X + 25Y <= 160*6

X >= 10

Y >= 15

Now that we have the objective functions we can solve this either using excel solver or manually. (For the purpose of haste, I will use the excel solver here. Screenshots attached below)

1. The most profitable number of each model of minicomputers are

Alpha 4 = 10

Beta 5 = 30

2. If they decide to make at least 15 of each model then we need to consider the sensitivity of the constraints. In this case the sensitivity shows a shadow price of -240 for every increase in 1 unit of the constraint. Hence if we increase the constraint from 10 to 15, it will decrease the profit by 240*5 = 1200. The current profit is 66720. It will become 66720-1200 = 65520.