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A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters alpha=3,theta=.5, where

A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters alpha=3,theta=.5, where theta is in units of days per 1000 units of rolls. It costs $2 to make a unit of rolls that sells for $5 on the first day when the rolls are fresh. Any leftover units are sold on the second day for $1. How many units should be made to maximize the expected value of the profit? I want to know whats the maximum profit

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