The XYZ corporation, a monopolist, receives a report from a consulting firm concluding that the demand function for its product is:
Q = 80 - 1.5P + 2.3M + 0.75A

Where Q is the number of units sold, P the price of its product, M is buyers' per capita income, and A is the firm's advertising expenditure. The firms' average cost function is:

AVC = 42 - 8Q + 1.5Q2

Consumer's per capita income is estimated to be $10,000 and the firm spends $200,000 on advertising. The firm's total fixed cost is equal to $50,000.

a. How much output should the firm produce to maximize profit (minimize loss)? Show all your work (steps and calculations)
b. What price should be charged for the output? Show all your work.
c. What is the firm's expected profit or loss? Show all your work