S14-26. Fun ’n Games is a large discount toy store in Fashion City
Mall. The store typically has slow sales in the summer
months that increase dramatically and rise to a peak at Christmas.
However, during the summer and fall, the store must
build up its inventory to have enough stock for the Christmas
season. In order to purchase and build up its stock during the
months when its revenues are low, the store borrows money.
Following is the store’s projected revenue and liabilities
schedule for July through December (where revenues
are received and bills are paid at the first of each month).
Month Revenues Liabilities
July $20,000 $60,000
August 30,000 60,000
September 40,000 80,000
October 50,000 30,000
November 80,000 30,000
December 100,000 20,000
At the beginning of July the store can take out a sixmonth
loan that carries an 11% interest rate and must be
paid back at the end of December. (The store cannot reduce
its interest payment by paying back the loan early.)
The store can also borrow money monthly at a rate of 5%
interest per month. Money borrowed on a monthly basis
must be paid back at the beginning of the next month.
The store wants to borrow enough money to meet its cash
flow needs while minimizing its cost of borrowing.
a. Formulate and solve a linear programming model for
b. What would be the effect on the optimal solution if
the store could secure a 9% interest rate for a 6-month
loan from another bank?