Demand for photocopying machines the weekly demand for the

Question

Question: DEMAND FOR PHOTOCOPYING MACHINES The weekly demand for the LectroCopy photocopying machine is given by the demand equation

p = 2000 - 0.04x              (0 ≤ x ≤ 50,000)

where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function for manufacturing these copiers is given by

C(x) = 0.000002x³ - 0.02x² + 1000x ^{+ 120,000}

where C(x) denotes the total cost incurred in producing x units.

a. Find the revenue function R, the profit function P, and the average cost function C¯.

b. Find the marginal cost function C', the marginal revenue function R, the marginal profit function P', and the marginal average cost function C¯'.

c. Compute C'(3000), R'(3000), and P'(3000).

d. Compute C'(5000) and C'(8000) and interpret your results.