The revenue and cost functions for producing as well as selling quantity x for the certain production facility are given below.
R(x) = 12x - x^{2}
C(x) = 18 + 3x
a) Find out the profit function P(x).
b) Employ Excel to graph the functions R(x), C(x) and P(x) for interval 0≤ x ≤ 10. Copy and paste the graph below. Note: Employ Scatter plot with smooth lines and markers.
c) Compute the break-even quantities.
d) Find out the marginal revenue R'(x).
e) Find out the marginal cost C'(x)
f) At what quantity is profit maximized?