Question

Suppose that q = D(p) = 800 - 5p is the demand function for a certain consumer item with p as the price in dollars for one unit of this item and q as the number of units. Find the greatest possible revenue by first finding the price p at which the marginal revenue becomes zero and then finding out the revenue that results at this price.
Answer choices:
a) 32000
b)12000
c)54000
d)64000
e)8000
F) none of the above

Answer 1

R = p q = p(800-5p) = 800 p - 5 p^2
dR/dp = 0 when R is max
dR/dp = 800 - 10 p
so max when p = 80
then find q
q = 800 - 5 (80) = 400
so the revenue at max = p q = 80 * 400 = 32,000