The manufacturer of a CD player has found that the revenue R

The manufacturer of a CD player has found that the revenue R (in dollars) is
R(p) = -5p2 + 1970p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue,
what is the maximum revenue to the nearest whole dollar?

a. $388,090
b. $1,552,360
c. $194,045
d. $776,180

Solution

R(p)=-5p²+ 1970p

The revenue is maximum at maximum value of p

and to find the maximum value of p,we have to use vertex formula which is -b/2a

Here b=1970 and a=-5

Therefore p=-1970/2(-5)

p = 197

The maximum value of p is 197

Therefore R(197)=-5(197)^2+ 1970(197)

                        = -5(38809)+ 388090

                       =-194045+ 388090= 194045

And the maximum revenue is $194045