The revenue and cost functions for producing and selling quantity x for a certai

Question

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?

Explanation / Answer

a) Profit = Revenue - Cost i.e. P(x)=R(x)-C(x) b)Enter the equations into excel and create a table from 0 to 12. From this it is very easy to plot a graph. c) Break-even points are the points at which one line intersects the other. d) Average cost = (total cost)/(quantity at break-even) e)Differentiate R(x) to get R'(x) f)Differentiate C(x) to get C'(x) g) Find the maximum on the value of profit on the curve, the corresponding quantity is the profit maximizing quantity.

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