Practice!

Sample Problem

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)=-25p2+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)

Solution

a)If f(x)=ax2+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