Liabilities $60,000 Month Revenues $20,000 July August September 30,000 60,000 40,000 80,000 October 50,000 30,000 November 80,000 30,000 December 100,000 20,000
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 Christ-
mas. 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 liabili-
ties
are received and bills are paid at the first of each month).
At the beginning of July the store can take out a six-
month loan that carries an 11% interest rate and must be
paid back at the end of December. (The store cannot re-
duce 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
this problem.
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?
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