Question

I need help for this maximizing revenue question please

Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is

R(p)= -4p^2+4000p

What unit price should be established for the dryer to maximize revenue? What is the maximum revenue?

Please be thorough as I'm studying for finals and have forgotten how to do it.

Answer 1

well because of the negative symbol in front of the 4p^2 we know that this is a upside down parabola so we know we're dealing with a maximum point (the point where we would get the maximum revenue)
so lets simplify the equation first to make it easier to solve
R(p)= -4 (p^2-1000p)
R(p)=-4p(p-1000)

With that simplified we know that the two x intercepts are 0 and 1000. So the answer should be right in the middle. or p= 500

Answer 2

any questions?

Answer 3

nope, thank you very much!