EJ Korvair Department Store has 1000 in available cash At th

E.J. Korvair Department Store has $1,000 in available cash. At the beginning of each of the next six months, E.J. will receive revenues and pay bills as shown in below table. It is clear that E.J. will have a short-term cash flow problem until the store receives revenues from the Christmas shopping season. To solve this problem, E.J. must borrow money. At the beginning of July, E.J. may take out a six-month loan. Any money borrowed for a six-month period must be paid back at the end of December along with 9% interest (early payback does not reduce the interest cost of the loan). E.J. may also meet cash needs through month-to-month borrowing. Any money borrowed for a one-month period incurs an interest cost of 4% per month. Use linear programming to determine how E.J. can minimize the cost of paying its bills on time.

Month   Revenues ($)   Bills ($)
July      1,000         5,000
August    2,000         5,000
September 2,000         6,000
October   4,000         2,000
November 7,000         2,000
December 9,000         1,000

Solution

July                 = X1

August            =X2

September       =X3

October          =X4

November     =X5

December    =X6

Minimize = 5,000 + 5,000 + 6,000+ 2,000+ 2,000 + 1,000

5,000 X1 + 5,000 X2 + 6,000 X3+ 2,000 X4+ 2,000 X5+ 1,000 X6 > 0.04

X1 +X2+X3+X4+X5+X6 < 0

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