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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 given by the inverse demand function P = 1,200 − 4Q, the utility 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) = 8,000 + 6Q12and C2(Q2) = 6,000 + 3Q22, respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits.

Answer 1

To determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits, we can use the given information to find the quantities that maximize profits and calculate the price and profits based on those quantities.

Step-by-step explanation:

The profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company's profits can be determined using the given information.

To maximize profits, the utility company should produce the quantities of electricity where the marginal cost equals the marginal revenue.

Marginal cost (MC) is the derivative of the cost function, and marginal revenue (MR) is the derivative of the demand function. Setting MC equal to MR and solving for Q1 and Q2 will give the optimal quantities.

Once the optimal quantities are known, the price can be determined by plugging them into the demand function.

The company's profits can be calculated by subtracting the total costs from the total revenue.