# Profit-maximizing amount, the optimal price

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern Florida. To meet monthly demand for electricity in these counties, which is represented by the inverse demand function, P = 1000 - 5 Q, the utility company has set up two electric generating facilities: Q â? kilowatts are produced at facility 1 and Qâ?? kilowatts are produced at facility 2 (so Q = Qâ?+ Q â?? & P = 1000 - 5(Q â? + Q â??)). The costs of producing at each facility are given by

Câ? (Q â?) = 10,050 + 5 Qâ?² and Câ?? (Q â??) = 5,000 + 2 Qâ?? ², respectively.

Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits.

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Below, find the steps necessary to determine the profit-maximizing amounts of electricity, the optimal price, and the utility company's profit:

I use Q for Q1 and q for ...

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This solution provides the profit-maximizing amount, the optimal price, and Company's profits.