I'm having trouble translating this problem into a workable form:
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.
At this point I am stuck as I am not sure what is what in the distribution. The remainder of the problem is as follows:
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 for \$1. How many units should be made to maximize the expected value of the profit?