# Ampco is a manufacturing company that has a contract to supply a customer with parts from April

## Question:

Month .......... Required Space (ft.2)

April ............ 47,000

May ............. 35,000

June ............. 52,000

July .............. 27,000

August ............ 19,000

September .......... 15,000

The rental agent Ampco is dealing with has provided it with the following cost schedule for warehouse space. This schedule shows that the longer the space is rented, the cheaper it is. For example, if Ampco rents space for all 6 months, it costs $1.00 per square foot per month, whereas if it rents the same space for only 1 month, it costs $1.70 per square foot per month:

Rental Period .............

(months) .......... $/ft.2/Month

6 ............ $1.00

5 ........... 1.05

4 ........... 1.10

3 ........... 1.20

2 ........... 1.40

1 ........... 1.70

Ampco can rent any amount of warehouse space on a monthly basis at any time for any number of (whole) months. Ampco wants to determine the least costly rental agreement that will exactly meet its space needs each month and avoid having any unused space.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.

c. Suppose that Ampco relaxed its restriction that it rent exactly the space it needs every month such that it would rent excess space if it was cheaper. How would this affect the optimal solution?

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## Step by Step Answer:

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