Suppose the demand function relating demand and price is given by p(x) = 50 0 005x

The total cost of

Question

Suppose the demand function relating demand and price is given by p(x) = 50 – 0.005x. The total cost of

making x units is given by C(x) = 0.00001X3 – 0.033×2 + 48X + 5,000

a) Find the revenue function R(x).

b) Find the profit function P(x).

c) How many units must be made and sold to maximize profit? Verify that you have found the maximum using the first derivative test. What is the maximum profit?

d) What are the marginal cost, marginal revenue and marginal profit when 1,000 units are made and sold?

e) What are the marginal cost, marginal revenue and marginal profit when 3,000 units are made and sold?

f) What are the marginal cost, marginal revenue and marginal profit when the number of units made and sold is the quantity found in c)?

Math