Problema Solution
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 provided by our tutors
Revenue = price*number of backpacks
R = p*(-2p + 50)
R = - 2p^2 + 50p
We need to find the maximum of the parabolic function: R = - 2p^2 + 50p
R max = -c - b^2/(4a), where a = -2, b = 50, c = 0
R max = - 0 - 50^2/(4*(-2))
R max = $312.50
p max = - b/(2a)
p max = - 50/(2*(-2))
p max = $12.50
$12.50 per backpack gives the maximum revenue; the maximum revenue is $312.50.