The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.
R(x) = 16x - x2
C(x) = 20 + 4x
a) Determine the profit function P(x).
b) Compute the break-even quantities.
c) Determine the average cost at the break-even quantities.
d) Determine the marginal revenue R'(x).
e) Determine the marginal cost C'(x)
f) At what quantity is the profit maximized?