Benjamin used regression analysis to fit quadratic relations to monthly revenue and cost data with the following results:

R  0.007Q2  32Q TC  0.004Q2  2.2Q  8

a. Plot R and TC. Estimate the quantity Q at which the maximum profit should occur. Estimate the profit at this quantity.

b. The profit relation Profit RTC and calculus can be used to determine the quantity Qp at which the maximum profit will occur, and the amount of this profit. The equations are:

Profit  aQ2  bQ  c Qpb2a Maximum profit  b24a  c Use these relations to confirm the graphical estimates you made in (a). (Your instructor may ask you to derive the relations above.)