STC 6000 + 12Q + 3Q? < Note: this is not a typical cubic function %3D a. Find the price function and then the TR function. See Assignment 3 or 4 for an example. Hint: another name for price is average revenue (AR). b. Write the MR and MC functions below. Remember: MR = dTR/dQ and MC = dSTC/dQ. See Assignment 5 for a review of derivatives. c. What positive value of Q will maximize total profit? Remember: Setting MR = MC and solving for Q will give you the Q that maximizes total profit. The value of Q you get should not be zero or negative. d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask per unit for each unit of Q that maximizes total profit. e. How much total profit will result from selling the quantity found in (c) at the price found in (d)? Remember: profit is TR – STC. f. At what level of Q is revenue maximized? Remember: let MR = 0 and solve for Q. MR = 0 signals the objective of maximizing revenue. g. At what level of Q is average profit per unit maximized? Hint: You found the profit function in (e) above. Average profit is the total profit function

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Please help with g.

The average revenue (demand) for product Q is given by AR = 400 – 2Q and the
total cost of Q by:
STC
6000 + 12Q + 3Q?
< Note: this is not a typical cubic function
%|
a. Find the price function and then the TR function. See Assignment 3 or 4
for an example. Hint: another name for price is average revenue (AR).
b. Write the MR and MC functions below. Remember: MR = dTR/dQ and
%3D
MC = DSTC/dQ. See Assignment 5 for a review of derivatives.
%3D
c. What positive value of Q will maximize total profit? Remember: Setting
MR = MC and solving for Q will give you the Q that maximizes total
profit. The value of Q you get should not be zero or negative.
d. Use the price function found in (a) to determine the price per unit that
will need to be charged at the Q found in (c). This will be the price you
should ask per unit for each unit of Q that maximizes total profit.
e. How much total profit will result from selling the quantity found in (c) at
the price found in (d)? Remember: profit is TR – STC.
f. At what level of Q is revenue maximized? Remember: let MR = 0 and
solve for Q. MR = 0 signals the objective of maximizing revenue.
g. At what level of Q is average profit per unit maximized? Hint: You found
the profit function in (e) above. Average profit is the total profit function
(e) divided by Q. To find the level of Q that maximizes average profit,
find the first derivative of the average profit function, set this derivative
equal to zero and solve for Q.
Transcribed Image Text:The average revenue (demand) for product Q is given by AR = 400 – 2Q and the total cost of Q by: STC 6000 + 12Q + 3Q? < Note: this is not a typical cubic function %| a. Find the price function and then the TR function. See Assignment 3 or 4 for an example. Hint: another name for price is average revenue (AR). b. Write the MR and MC functions below. Remember: MR = dTR/dQ and %3D MC = DSTC/dQ. See Assignment 5 for a review of derivatives. %3D c. What positive value of Q will maximize total profit? Remember: Setting MR = MC and solving for Q will give you the Q that maximizes total profit. The value of Q you get should not be zero or negative. d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask per unit for each unit of Q that maximizes total profit. e. How much total profit will result from selling the quantity found in (c) at the price found in (d)? Remember: profit is TR – STC. f. At what level of Q is revenue maximized? Remember: let MR = 0 and solve for Q. MR = 0 signals the objective of maximizing revenue. g. At what level of Q is average profit per unit maximized? Hint: You found the profit function in (e) above. Average profit is the total profit function (e) divided by Q. To find the level of Q that maximizes average profit, find the first derivative of the average profit function, set this derivative equal to zero and solve for Q.
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