Modem Corporation of America (MCA) is the world's largest producer of modem communication devices for microcomputers. MCA sold 9,000 of the regular model and 10,400 of the smart ("intelligent") model this September. Its income statement for the month is shown in the table on this page. Costs presented are typical of prior months and are expected to remain at the same levels in the near future.

The firm is facing several constraints as it prepares its November production plan. First, it has experienced a tremendous demand and has been unable to keep any significant inventory in stock.

This situation is not expected to change. Second, the firm is located in a small Iowa town from which additional labor is not readily available. Workers can be shifted from production of one modem to another, however. To produce the 9,000 regular modems in September required 5,000 direct labor hours. The 10,400 intelligent modems absorbed 10,400 direct labor hours.

MCA Income Statement Month Ended September 30

Third, MCA is experiencing a problem affecting the intelligent modems model. Its component supplier is able to guarantee only 8,000 microprocessors for November delivery. Each intelligent modem requires one of these specially made microprocessors. Alternative suppliers are not available on short notice. MCA wants to plan the optimal mix of the two modem models to produce in November to maximize profits for MCA.
(a) Formulate, using September's data, MCA's problem as a linear program.
(b) Solve the problem graphically.
(c) Discuss the implications of your recommendedsolution.

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REGULAR INTELLIGENT MODEMS MODEMS Warranty replacements Selling and general expenses General expenses-variable 30,000 General expenses fixed Sales commissions Total operating cost Income taxes (25%)