A shoe store sells about 200 pairs of a new basketball shoe each month when it charges $60 per pair. For each $1 increase in price, about 2 fewer pairs per month are sold. How much per pair should the store charge to maximize monthly revenue? What is the maximum revenue?
+36916
Increase price 1 2 fewer pairs sold
for 'x' dollar increase:
Price * pairs sold = revenue
(60 + x) * (200-2x) = revenue
12000 -120x + 200x -2x^2 = revenue
-2x^2+80x+12000 = revenue This will be an upside down parabola (due to the -2x^2)
Maximum will be at -b/2a a = -2 b = 80
80/4 = $ 20 this is the mumber of 1 $ increases.....so $80 per pair will maximize profit
Plug in that price x pairs sold
$80 x ( 200 - 2(20)) = max revenue
