Abakery sells rolls in units of a dozen. the demand x (in 1000 units) for rolls has a gamma distribution with parameters α = 3, θ = 0.5, where θ 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?