The average revenue (demand) for product Q is given by AR = 50 - Q and the total cost of Q by:
STC = 100-4Q+2Q^2
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, letting MR = MC signals the objective of total profit maximization. Solve MR = MC for Q. 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 for the total profit maximizing quantity.
e. What total profit will result from selling the quantity found in (c) at the price found in (d)? Hint: the profit function is found as TR â STC.
The average revenue (demand) for product Q is given by AR = 50 - Q and the total cost of Q by:
STC = 100-4Q+2Q^2
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, letting MR = MC signals the objective of total profit maximization. Solve MR = MC for Q. 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 for the total profit maximizing quantity.
e. What total profit will result from selling the quantity found in (c) at the price found in (d)? Hint: the profit function is found as TR â STC.
