You manage a firm that operates as a monopoly. Your firm faces the following demand for the product you sell:

Q=303.96-0.4P+0.02M-4P_R

where P is the good's price, M is the annual average household income level and P_R is the price per unit of a related product. Currently, M = $52,000 and P_R = $1.25. Economists at your firm have estimated the average variable cost function to be:

AVC=40+0.002Q²-0.3Q

a.At the current levels for M and P_R, find your firm's total revenue and marginal revenue functions. (Remember, total and marginal revenue should be a function of quantity and not price.)

b.Find your firm's total variable and marginal cost functions.

c.If you want to maximize your profit, what is the optimal price to charge for your product and how many units will you sell?

d.If this firm's total fixed costs are $2,500, how much profit will it earn? Should this firm stay in business? Why or why not?