SOLUTION: Jeremy sells 120 handmade ornaments per week at $4 per ornament. For each $0.50 decrease in price, he can sell 20 more ornaments. a) Write an equation for his revenue. b) What pr

Algebra ->  Trigonometry-basics -> SOLUTION: Jeremy sells 120 handmade ornaments per week at $4 per ornament. For each $0.50 decrease in price, he can sell 20 more ornaments. a) Write an equation for his revenue. b) What pr      Log On


   

Question 1080657: Jeremy sells 120 handmade ornaments per week at $4 per ornament. For each $0.50 decrease in price, he can sell 20 more ornaments.
a) Write an equation for his revenue.
b) What price should Jeremy charge to maximize revenue?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
PRICE    ORNAMENTS
 4         120
 3.5       120+20
 3.0       120+20+20
 2.5       120+20+20+20
 .
 .
 4-0.5x   120+20x

Revenue, %284-0.5x%29%28120%2B20x%29, x is the number of $0.50 decreases from initial $4 price. 4-0.5x%3E0 or 4%3E0.5x, highlight_green%28x%3C8%29.

highlight%28r%28x%29=%284-0.5x%29%28120%2B20x%29%29

Maximum is exact middle of the zeros of r.
-
120%2B20x=0
6%2Bx=0
x=-6, by itself, not an acceptable value for x.
-
4-0.5x=0
4=0.5x
x=8
-
Exact middle of the zeros: %28-6%2B8%29%2F2=2%2F2=highlight_green%281%29

Maximum revenue would be at x=1, or 4-0.5=highlight%283.50%29 dollars per ornament.