3. (5 points) The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet the monthly demand for electricity in these counties, which is represented by the estimate inverse demand function P = 1,200 - 4Q, marginal revenue function is MR = 1,200 - 8Q, the utility company has set up two electricity generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing electricity at each facility are estimated as CI(Q1) = 8,000 + 6Q12 and MC1 = 12Q1 and C2(Q2) = 6,000 + 3Q22 and MC2 = 6Q2, respectively. Determine the profit maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits. Please show your calculations