NAME ____________________(6) Due _____________ Show work for credit! The demand for product Q is given by Q = 350 - .25P and the total cost of Q by: STC = 20000 + 200Q - 9Q2 + 1/3Q3 a. Find the price function and then the TR function. See Assignment 3 or 4 for an example. 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
NAME ____________________(6) Due _____________ Show work for credit!
The demand for product Q is given by Q = 350 - .25P and the total cost of Q by:
STC = 20000 + 200Q - 9Q2 + 1/3Q3
a. Find the
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 positive level of Q is marginal profit maximized? You found the profit function in (e) above. Marginal profit is the first derivative of the profit function (e). Next, find the derivative of marginal profit, set it equal to zero, and solve for Q.
h. What price per unit should be charged for each unit of Q found in (g)? Simply plug the Q you got in (g) into the same price function you found in (a) and also used in (d).
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