Question: Problem 3

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) Use Excel to graph the functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.

c) Compute the break-even quantities.

d) Determine the average cost at the break-even quantities.

e) Determine the marginal revenue R’(x).

f) Determine the marginal cost C’(x)

g) At what quantity is the profit maximized?