Corsouth Mortgage Associates is a large home mortage firm in

Corsouth Mortgage Associates is a large home mortage firm in the Southeast. It has a poll of permanent and temporary computer operators who process mortgage accounts, including posting payments and updating escrow accounts for insurane and taxes. A permanent operator can process 220 accounts per day, and a tempory operator can process 140 accounts per day. On average, the firm must process and update at least 6, 300 accounts daily. The company has 32 computers workstations available. Permanent and temporary operators work 8 hours a day. A permanent operator average about .4 erros per day, whereas a temporary operator average 0.9 error per day. The copmay wants to limit errors to 15 per day. Corsouth wants to determine the number of permanent and temporary operators it needs to minimize cost. Formulate, and solve an intereger programming model for this problem and compare this solutin to the non-integer solutions.

Solution

First tabulate all the information given.

Thus objective is to minimize cost :

Constraints are

0.4x+0.9y <=15 and

220x+140y>=6300

Also x+y <=32

The graph is shown above.

Integral solutions would be (0,45) (25,5)(28,0)

Non integral solutions would be (0,45) (25.14,5.49)(28.64,0)