The Zig-Zag Manufacturing Company produces two products, zigs and zags. Each of

Question

The Zig-Zag Manufacturing Company produces two products, zigs and zags. Each of these products has to be processed through all three of its machines, as shown in the table. If Zig-Zag makes $12 profit on each zig and $8 profit on each zag, find the number of each that the company should make in order to maximize its profit.

12.       A nutritionist is designing a meal for one of her patients. The meal must include two vegetables, A and B, but not more than 100 g of each. Suppose that each 10-g portion of A contains 2 units of iron and 2 units of vitamin B12, and each 10-g portion of B contains 1 unit of iron and 5 units of vitamin B12. The number of calories in each 10-g portion of these vegetables is 5 for A and 3 for B. If the patient needs at least 20 units of iron and 36 units of vitamin B12 in the meal, how many grams of each vegetable should the nutritionist include to satisfy the iron and vitamin requirements while minimizing the number of calories in the meal?

           

16. A local television station is faced with a problem. It found that program A with 20 min of music and 1 min of commercials draws 30,000 viewers, whereas program B with 10 min of music and 1 min of commercials draws 10,000 viewers. The sponsor insists that at least 6 min per week be devoted to his commercials, and the station can afford no more than 80 min of music per week. How many times per week should each program be run to obtain the maximum number of viewers?

Explanation / Answer

DECISION VARIABLES NO.OF ZIGS TO BE MADE X NO.OF ZAGS TO BE MADE Y M-1 HOURS REQUIRED 4X+12Y M-2 HOURS REQUIRED 8X+8Y M-3 HOURS REQUIRED 6X PROFIT FUNCTION =P= 12X+8Y TO BE MAXIMIZED CONSTRAINTS M-1 HRS = 4X+12Y

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