Answer:
a. 1620-x^2
b. x=810
c. Maximum value revenue=$656,100
Step-by-step explanation:
(a) Total revenue from sale of x thousand candy bars
P(x)=162 - x/10
Price of a candy bar=p(x)/100 in dollars
1000 candy bars will be sold for
=1000×p(x)/100
=10*p(x)
x thousand candy bars will be
Revenue=price × quantity
=10p(x)*x
=10(162-x/10) * x
=10( 1620-x/10) * x
=1620-x * x
=1620x-x^2
R(x)=1620x-x^2
(b) Value of x that leads to maximum revenue
R(x)=1620x-x^2
R'(x)=1620-2x
If R'(x)=0
Then,
1620-2x=0
1620=2x
Divide both sides by 2
810=x
x=810
(C) find the maximum revenue
R(x)=1620x-x^2
R(810)=1620x-x^2
=1620(810)-810^2
=1,312,200-656,100
=$656,100
