How many units should be made to maximize the expected value of the profit? 3.2-19. A bakery

How many units should be made to maximize the expected value of the profit?

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3.2-19. A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distri- bution with parameters a 3,0 = 0.5, where is in units of days per 1000 units of rolls. It costs $2 to make a unit 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? 3.2-19. A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distri- bution with parameters a 3,0 = 0.5, where is in units of days per 1000 units of rolls. It costs $2 to make a unit 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?