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A monopolist supply electricity in a small town, it has two plants for generating electricity. The total costs of supplying electricity from each plant are

A monopolist supply electricity in a small town, it has two plants for generating electricity. The total costs of supplying electricity from each plant are as follows:

Plant1:TC(Q1)=50Q1

Plant2:TC(Q2)=20Q2+2Q22

whereQ1andQ2are units of output in plants 1 and 2 respectively. The monopolist faces the following market demand curve:P(Q) = 4004QwithQ=Q1+Q2. Find the profit maximizing quantity produced by each plant and the price charged by the monopolist.

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