Benjamin used regression analysis to fit quadratic relations to monthly revenue, R, and total cost, TC, data with the following results, where Q is quantity. R = −0.008Q2 + 32Q TC = 0.005Q2 + 2.2Q + 10 (a) Plot R and TC. Estimate the quantities QBE and Qp, where 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 Qp at which the maximum profit will occur and the amount of this profit. The equations are: Profit = aQ2 + bQ + c Qp = −b/2a Maximum profit = −b2/4a + c Use these relations to confirm your graphical estimate of QP. (Your instructor may ask you to derive the relations above.)
Benjamin used regression analysis to fit quadratic
relations to monthly revenue, R, and total cost, TC,
data with the following results, where Q is quantity.
R = −0.008Q2 + 32Q
TC = 0.005Q2 + 2.2Q + 10
(a) Plot R and TC. Estimate the quantities QBE
and Qp, where 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 Qp
at which the maximum profit will occur and
the amount of this profit. The equations are:
Profit = aQ2 + bQ + c
Qp = −b/2a
Maximum profit = −b2/4a + c
Use these relations to confirm your graphical
estimate of QP. (Your instructor may ask you to
derive the relations above.)
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
