Engineering Economy 7th Edition by Leland Blank ,Anthony Tarquin

Exercise 65

Benjamin used regression analysis to fit quadratic relations to monthly revenue and cost data with the following results:
R = -0.007 Q 2 + 32 Q
TC = 0.004 Q 2 + 2.2 Q + 8
a) Plot R and TC. Estimate the quantity Q p at which the maximum profit should occur. Estimate the amount of profit at this quantity.
b) The profit relation P = R - TC and calculus can be used to determine the quantity Q p at which the maximum profit will occur and the amount of the profit. The equations are
Profit = a Q 2 + bQ + c
Maximum profit =
Use these relations to confirm the graphical estimates you made in
a). (Your instructor may ask you to derive the relations above.)