Ampco is a manufacturing company that has a contract to supply a customer with parts from April through September. However, Ampco does not have enough storage space to store the parts during this period, so it needs to lease extra warehouse space during the 6-month period. Following are Ampco’s space requirements:
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?