SOLUTION: My question was already answered by Charles I think and he did an awesome job but he didn't tell me what the variables were so now i can't figure it out! Here's the question. If yo

Question 389358: My question was already answered by Charles I think and he did an awesome job but he didn't tell me what the variables were so now i can't figure it out! Here's the question. If you can somewhat explain it, that'd be great.
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?
Thanks in advance!
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
"My question was already answered by Charles I think and he did an awesome job but he didn't tell me what the variables were so now i can't figure it out! Here's the question. If you can somewhat explain it, that'd be great.
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?
Thanks in advance!"
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?

number of televisions (T) * materials/televison (100) + number of DVD players (D) * materials/DVD player (50) = $1000 per week --> 100T + 50D = 1000
number of televisions (T) * hours/television (2) + number of DVD players (D) * hours/DVD player (3) = 40 hours --> 2T + 3D = 40
number of televisions (T) * profit/television (300) + number of DVD players (D) * profit/DVD player (150) = total profit per week --> 300T + 150D
number of televisions (T) * sales price/televison + number of DVD players (D) * sales price/DVD player = total sales in a week

profit = sales - costs
costs + profit = sales (this equation rearranging of above equation)
costs = sales - profit (also rearranging of above equation)

let W = employee's wage/hr
television --> 2 * wage/hr + 100 + 300 = 2W + 400 --> sales price per television
DVD ---------> 3 * wage/hr + 50 + 150 = 3W + 200 --> sales price per DVD player

let T = televisions, let D = DVD players

100T + 50D = 1000 (total materials cost)
2T + 3D = 40 (total hours) -->

T = (40 - 3D)/2 --> substitute into 100T + 50D = 1000
100 * (40 - 3D)/2 + 50D = 1000
50 * (40 - 3D) + 50D = 1000 (above line simplified)
2000 - 150D + 50D = 1000 (distributed the 50)
2000 - 100D = 1000 (above line simplified)
-100D = -1000
100D = 1000
D = 10 DVD players

2T + 3D = 40 --> 2T + 30 = 40 (plugged in 10 for D)
2T = 10
T = 5 televisions

materials: 100T + 50D = 1000 --> 500 + 500 = 1000 (plugged in values for D and T)

5 televisions, and 10 dvd's

5 * (2W + 400) + 10 * (3W + 200) (plugged in sales prices)
10W + 2000 + 30W + 2000

40W + 4000 --> total sales in a week

total profit in a week: 300T + 150D = 5 * 300 + 10 * 150 = 1500 + 1500 = $3000

costs to make television plus pay employee = 40W + 4000 - 3000 = 40W + 1000

Hope this helps

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