A monopolist has a marginal cost function, 6Q 2 + 5Q, and the fixed costs are 25.

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A monopolist has a marginal cost function, 6Q2 + 5Q, and the fixed costs are 25. The demand function is 2P + Q = 510.
(a) Find an expression for the profit function in terms of Q.
(b) Hence find the production level that maximises profit and explain why this is a maximum.

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