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A monopoly operates three plants with total cost schedules TC1 = 40 + 0.1q1 + 0.04q2 TC2 = 18 + 3q2 + 0.02q2 2 TC3 = 30 + 4q3 + 0.01q2 3 and faces the market demand schedule p = 250 − 2q where q = q1 + q2 + q3 Set up the profit function and then use it to determine how much the firm should make in each plant to maximize profit, using the Hessian to check that second-order conditions are met.
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