A monopolist's inverse demand function is estimated asP= 150 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 isMC₁(Q₁) = 6Q₁, and the marginal cost of producing at facility 2 isMC₂(Q₂) = 2Q₂.

a. Provide the equation for the monopolist's marginal revenue function. (Hint:Recall thatQ₁+Q₂=Q.)

MR(Q) =Q₁Q₂

b. Determine the profit-maximizing level of output for each facility.

Output for facility 1:

Output for facility 2:

c. Determine the profit-maximizing price.