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.

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.