The Sentry Lock Corporation sells a variety of electronic goods through television shows. The company has a number of storage to keep the goods it sells but also takes out a lease on additional storage space when required. During the next 5 months the company anticipates that it is going to need to take out a lease on the following amounts of additional storage space: Month 1 2 3 4 5 Square Feet(ft2) Needed 20,000 30,000 40,000 35,000 50,000 At the beginning of any month the company can take out a lease on additional space for one or more months at the following costs: 

Lease Term (months) 1 2 3 4 5 

Cost per Sq. Ft. Leased $55 $85 $130 $165 $185 

Therefore, for example, at the beginning of month 1, the company can take out a lease on as much space as it requires for four months at a cost of $165 per ft2. Similarly, at the beginning of month 3, it can take out a lease on any amount of space for two months at a cost of $85 per ft2. The company needs to determine the optimal way of satisfying its storage requirements over the coming five months. 

a. Formulate an optimization model for this problem algebraically. 

b. Formulate and solve an optimization model for this problem on a spreadsheet. 

c. How much will it cost the company to satisfy its space requirements if each month it takes out a lease for one month exactly on the amount of space needed for the month?