The demand function for a firm with market power is estimated to be Q = 127,000 - 600P + 4M +11,000PR, where Q is output, P is price per unit, M is income, and PR the price of a related good. The manager estimates the values of M and PR will be $32,000 and $4, respectively, in 2008. The firm faces an average variable cost function estimated to be AVC = 600 - 0.05Q + 0.000001Q2. For 2008, determine the inverse demand function and the marginal revenue function, and the marginal cost function. Determine what the optimal level of output is for the firm and the firm’s profit if fixed costs are expected to be $4.0 million.