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A manufacturing firm can produce 1, 2, or 3 units of a product in a month, but the demand is uncertain. The demand is a discrete random variable that can take a value of 1, 2, or 3 with probabilities 0.2, 0.2, and 0.6, respectively.
If the unit cost of production is $400, unit revenue is $1000, and unit cost of unfulfilled demand is $0, determine the output that maximizes the expected total profit.