You have decided to start a business that makes portable mono speakers.

The total revenue R earned (in thousands of dollars) is given by

R(p)=-25p^{2}+1200p
where p is the price per unit (in dollars)

a) Find the unit price that will yield maximum revenue p (in dollars)= $

b) What is the maximum revenue? R (in thousands of dollars)= $

(round to nearest whole dollar)

a)If
f(x)=ax^{2}+bx+c and a<0, f has a maximum at x=-b/2a. The maximum
value is f(-b/2a)

a=-25, b=1200, c=0

maximum at p=-b/2a=-1200/(2*-25)=-1200/-50=24 (p=$24/unit for maximum revenue)

b)R(24)=-25(24)^{2}+1200(24)=14400.

14400=R where R is in thousands of dollars