Question: Tommy’s Toy Train Company is looking to expand. They will need to rent extra warehouse space over the next year until their new facility is constructed. Their capacity needs vary from month to month because the toy train industry has varying demands throughout the year. Because of economies of scale, it may be cheaper to rent excess capacity some months and have that capacity carry over into subsequent (higher demand) periods. Given the following data, formulate a mathematical program to determine how much capacity TTTC should lease each month.

Month Required Capacity (sq. feet)

1 30,000
2 20,000
3 40,000
4 10,000
5 50,000
6 50,000
7 40,000
8 10,000
9 30,000
10 20,000
11 40,000
12 50,000

Leasing Period Cost per Square Foot

(number of months)

1 $65
2 $100
3 $135
4 $160