Question

The total revenue R earned (in dollars) from producing a gift box of candles is given by R(p)=-10p^2+800p, where p is the price per unit.
a. Find the revenues when the prices per box are $20, $25, and $30
b. Find the unit price that will yield a maximum revenue. What is the maximum revenue? Explain your results.

Answer 1

A.) R(20) = -10(20)^2 + 800(20) = -10(400) + 16000 = -4000 + 16000 = $12,000

R(25) = -10(25)^2 + 800(25) = -10(625) + 20000 = -6250 + 20000 = $13,750

R(30) = -10(30)^2 + 800(30) = -10(900) + 24000 = -9000 + 24000 = $15,000

b.) For maximum revenue, dR/dp = 0
dR/dp = -20p + 800 = 0
20p = 800
p = 40

Therefore, the maximum revenue will be recorded when the price is set at $40.