The weekly total cost (In dollars) incurred by Pulsar for producing sets is represented by the following values: c(x) = 0.00001x^2 + 0.02x + 70,000.
(a) Find the revenue function R(x):
R(x) = 190x + 0.005x^2 + 2.
(b) Find the profit function P(x):
P(x) = R(x) - c(x).
(c) Find the marginal cost function c'(x):
c'(x) = 0.00002x + 0.02.
(d) Find the marginal revenue function R'(x):
R'(x) = 190 + 0.01x.
(e) Find the marginal profit function P'(x):
P'(x) = R'(x) - c'(x).
Compute the following values (rounded to two decimal places):
c'(3,000), R'(3,000), P(3,000).
(f) Sketch C(x).