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 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?