A Monopolists inverse demand function is P = 150 - 3Q. The company produces output at two facilities; the cost of producing in plant 1 is C1 = 40 + 3Q1^2 and the cost of producing in plant 2 is C2 = 50 + Q2^2.
a. Provide the equation for the monopolist's marginal revenue function (Note: Q = Q1 + Q2)
b. Determine the profit maximizing level of price and output for each facility