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

R = – 0.007 Q2 + 32 Q

TC = 0.004 Q2 + 2.2 Q + 8

(a) Plot R and TC. Estimate the quantity Qp 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 = aQ2 + bQ + c

Qp = –b/2a

Maximum profit = –b2/4a + c

Use these relations to confirm the graphical estimates you made in (a).