Question

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price mc023-1.jpg number of backpacks.)
$9.00 per backpack gives the maximum revenue; the maximum revenue is $32.00.
$12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.
$12.50 per backpack gives the maximum revenue; the maximum revenue is $312.50.
$15.00 per backpack gives the maximum revenue; the maximum revenue is $20.00.

Answer 1

Revenue R(p) = p(−2p + 50) = −2p^2 + 50p, a downward-opening parabola. Its vertex is at p = −b/(2a) = −50/(2·−2) = 12.5.

So the price that maximizes revenue is $12.50, and the maximum revenue is R(12.5) = 12.5·25 = $312.50.

(Third choice.)