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.

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.

anonymous · Answer

Part a is simply plug and chug stuff that you should use a calculator to solve. Part b, however, requires either a graph of the equation or its derivative. If you're looking to use the latter, set it (-20p+800) equal to zero to solve for the price that maximizes revenue.

anonymous · Answer

??

anonymous · Answer

I got part a, but when i graphed part b I got a straight line and not a parabola. do you have any idea why I'm getting that?

anonymous · Answer

Did you graph the equation I gave you or the one you had to start?

anonymous · Answer

The derivative should work for b
-20p+800=0
-20p=-800
p=40

anonymous · Answer

I don't mean to overwhelm you, but, since this problem is a parabola facing downwards, the max is the vertex; so you could find your max by completing the square as well. Would that be easier?

anonymous · Answer

ok that would be easier thank you I got it now!

anonymous · Answer

yw ;)