The largest public utility company in New South Wales (NSW) is the sole provider of electricity across all regions in the state. The monthly demand for electricity in NSW is given by the inverse demand function P = 1,000 - 5Q. The electricity company has set up two electric 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 given by C₁(Q₁) = 10,050 + Q₁2 and C₂(Q₂) = 5,000 + 2Q₂², respectively.

a. Determine the profit-maximising amounts of electricity to produce at the two facilities.

b. Determine the optimal price.

c. Determine the utility company's profits.