Assume that a monopolist faces a demand curve for its product given by:

p=703q

Further assume that the firm's cost function is:

TC=510+8q

Hint 1:Define a formula for Total Revenue using the demand curve equation.

Hint 2:The first derivative of the total profit function, which is cumulative, is the marginal profit function, which is incremental. The lecture and formula summary explain how to compute the derivative.

Set the marginal profit equal to zero to define an equation for the optimal quantity q.

Hint 3:When computing the total profit for a candidate quantity, use the total profit function you define (rather than summing the marginal profits using the marginal profit function).

How much output should the firm produce? Please round your answer to the nearest hundredth.

What price should the monopolist choose to maximize profits? Please round your optimal price answer to the nearest hundredth.

What is the profit for the firm at the optimal quantity and price? Please round your optimal profit answer to the nearest integer.