**PLEASE EXPLAIN HOW TO COME UP WITH THE OBJECTIVE FUNCTION (PROFIT FUNCTION) THIS QUESTION WAS PREVIOUSLY SOLVED, BUT THE TUTOR DID NOT EXPLAIN HOW HE CAME UP WITH THE PROFIT FUNCTION. THE OBJECTIVE FUNCTION: PROFIT = 22.67X1 +29.01X2 DOES NOT MAKE SENSE.

Modem Corporation of America (MCA) is the worlds 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

	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 0	76,80
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 expensesvariable	30,000	35,000
General expensesfixed	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	$139,41

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 Septembers data, MCAs problem as a linear program.

(b) Solve the problem graphically.

(c) Discuss the implications of your recommended solution.