The demand for product Q is given by Q = 385 - P and the total cost of Q by

STC = 3000 + 40Q -5Q2 + 1/3Q2

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, 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.