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

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