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Suppose that any firm intending to produce SOMA must build an integer number of plants: 0, 1, 2,

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Suppose that any firm intending to produce SOMA must build an integer number of plants: 0, 1, 2, .... Building Q plants costs each firm 3.5Q dollars.

Each plant produces one unit of SOMA.

If firm 1 builds Q1 plants and firm 2 builds Q2 plants, the market price (p) for one unit of SOMA will be 6 - (Q1 + Q2).

If there was a single firm capable of producing SOMA, how many plants would it install to maximize profit?