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