A clothing manufacturer hass 600yd of cloth available to make shirts and decorat

Question

A clothing manufacturer hass 600yd of cloth available to make shirts and decorated vests. Each shirt requires 3yd of material and provides a profit of $5. Each vest requires 2yd of material and provides a profit of $2. The manufacturer wants to guarantee that under all circumstances, there are minimums of 100 shirts and 30 vests produced. How many of each garment should be made to maximize profit? If there are no minimum quantities,how, if at all, does the optimal production policy change?

Make the following changes to the problem:

1.) Develop a LP model with the minimum quantity requirements (refers to the text problem's first question).

2.) Modify the model you developed above assuming there are no minimum quantities (refers to the text problem's second question)

Note: Develop the LP models only. Do not attempt to solve them.

Explanation / Answer

Let the number of shirts manufactured be x

Let the number of vest manufactured be y

With minimum quantities of shirts and vests

2.     y >= 30

3.     3x + 2y <= 600

4.     Maximise (5x + 2y)

With no minimum quantities of shirts and vests

2.     Maximise (5x + 2y)

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