Question 389087: A company makes two products, televisions and DVD players. The televisions require two hours of labor and $100 of materials per television. The profit per television is $300. The DVD player requires three hours of labor and $50 of materials per DVD player. The profit per player is $150. The company can afford to spend $1000 each week for the cost of the material. If an employee works forty hours a week, how many televisions and/or DVD players should the employee make in order to maximize the company's profit?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! A company makes two products, televisions and DVD players. The televisions require two hours of labor and $100 of materials per television. The profit per television is $300. The DVD player requires three hours of labor and $50 of materials per DVD player. The profit per player is $150. The company can afford to spend $1000 each week for the cost of the material. If an employee works forty hours a week, how many televisions and/or DVD players should the employee make in order to maximize the company's profit?
profit = sales - costs
costs + profit = sales
television --> 2 * wage/hr + 100 + 300 = 2W + 400
DVD ---------> 3 * wage/hr + 50 + 150 = 3W + 200
100T + 50D = 1000 (materials)
2T + 3D = 40 (hours) --> T = (40 - 3D)/2 --> substitute into 100T + 50D = 1000
100 * (40 - 3D)/2 + 50D = 1000
50 * (40 - 3D) + 50D = 1000
2000 - 150D + 50D = 1000
2000 - 100D = 1000
-100D = -1000
100D = 1000
D = 10
2T + 3D = 40 --> 2T + 30 = 40
2T = 10
T = 5
100T + 50D = 1000 --> 500 + 500 = 1000
5 televisions, and 10 dvd's
5 * (2W + 400) + 10 * (3W + 200)
10W + 2000 + 30W + 2000
40W + 4000
profit: 5 * 300 + 10 * 150 = 1500 + 1500 = $3000
costs to make television plus pay employee = 40W + 1000
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