A manufacturing company has a contract to supply a customer

A manufacturing company has a contract to supply a customer with parts from April through September. However, the company 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. The space requirements are shown in Exhibit 4. The rent agent has provided the company with a cost schedule (see Exhibit 5) for warehouse space. This schedule shows that the longer the space is rented, the cheaper it is. For example, if the company rents space for all 6 months, it costs $1.00/ft.2 per month, whereas if it rents the same for only 1 month, it costs $1.70/ft.2 per month. The company can rent any amount of warehouse space on a monthly basis at any time for any number of (whole) months. The company 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. Suppose that the company were to relax its restriction that it rent exactly the space it needs every month such that it would rent excess space if it were cheaper. How would this affect the optimal solution? 

Month Required Space (ft.2 ) 

April 47,000 

May 35,000 

June 52,000 

July 27,000

 August 19,000 

September 15,000 

Exhibit 5 

Rental period (months) $/ft.2 /month 

6 1.00 

5 1.05 

4 1.10 

3 1.20 

2 1.40 

1 1.70