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?