math question about demand, revenue......

Question

3) If the price-demand function is given by d(x) = 120 + .01x - .002x^2

a. [1 point] Determine the revenue function R(x)

b. [3 points]Find and interpret R’(100)

Answer 1

d(x) = 120+ .01x - .02x^2

R(x) = revenue = price times quantity purchased

=xd(x) where x = price and d(x) = quantity

= 120x + .01x^2 - .02x^3

R'(x) = marginal revenue = MR = 120 + .02x - .06x^2

R'(100) = 120 + 2 - .06(10,000) = 122-600=-478

at price = 100, revenue decreases by 478

maximum profit is where MR=MC, where marginal revenue= marginal cost