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The manager of a two plant firm needs to decide how much to

The manager of a two plant firm needs to decide how much to produce in each plant. According to an economist the demand curve for the firm's product was estimated to be P = 78 - 15Q, Q is equal to the output in plan 1 plus output in plant 2 such that Q = Q₁ + Q₂. You are also given the marginal costs that characterize both plants. As such, MC₁ = 3Q₁ and MC₂ = 2Q₂.

How much output should be produced in plant 1 in order to maximize profits?

How much output should be produced in plant 2 in order to maximize profits?

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