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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?
Chain Rule : If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x). Proof We will s
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