Marginal cost revenue and profit the weekly demand for the

Question

Question: MARGINAL COST, REVENUE, AND PROFIT The weekly demand for the Pulsar 25 color LED television is

p = 600 - 0.05x            (0 ≤ x ≤ 12,000)

where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing the Pulsar 25 is given by

C(x) = 0.000002x³ - 0.03x² + 400x + 80,000

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

a. Find the revenue function R and the profit function P.

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

c. Compute C'(2000), R'(2000), and P'(2000) and interpret your results.

d. Sketch the graphs of the functions C, R, and P and interpret parts (b) and (c), using the graphs obtained.