=7-43 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 for Problem 7-43. 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.

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.

Table for Problem 7-43 MCA Income Statement Month Ended September 30 Regular Modems Intelligent Modems Sales $450,000 $640,000 Less: Discounts 10,000 15,000 Returns 12,000 9,500 Warranty replacements 4,000 2,500 Net sales $424,000 $613,000 Sales costs Direct labor 60,000 76,800 Indirect labor 9,000 11,520 Materials cost 90,000 128,000 Depreciation 40,000 50,800 Cost of sales $199,000 $267,120 Gross profit $225,000 $345,880 Selling and general expenses General expenses—variable 30,000 35,000 General expenses—fixed 36,000 40,000 Advertising 28,000 25,000 Sales commissions 31,000 60,000 Total operating cost $125,000 $160,000 Pretax income $100,000 $185,880 Income taxes (25%) 25,000 46,470 Net income $ 75,000 $139,410 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 recommended solution.