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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.
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