The Shop at Home Network sells various household goods during live television broadcasts. The company owns several warehouses to hold many of the goods it
sells, but also leases extra warehouse space when needed. During the next five
months the company expects that it will need to lease the following amounts of extra
warehouse space:
Month 1 2 3 4 5
Square Feet Needed 20,000 30,000 40,000 35,000 50,000
At the beginning of any month the company can lease extra space for one or more
months at the following costs:
Lease Term (months) 1 2 3 4 5
Cost per Sq. Ft. Leased $55 $95 $130 $155 $185
So, for instance, at the start of month 1 the company can lease as much space as it
wants for 4 months at a cost of $155 per square foot. Similarly, at the start of month 3
it can lease any amount of space for 2 months at a cost of $95 per square foot. The
company wants to determine the least costly way of meeting its warehousing needs
over the coming 5 months.
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem and solve it using Solver.
c. What is the optimal solution?
d. How much would it cost the company to meet its space needs if in each month it
leases for one month exactly the amount of space required for the month