2. Joseph must order each year's calendar in August for delivery and eventual sale by December 31st. In previous years, standard Business Calendar sales have ranged from a low of 2000 to a high of 2300, so assume that demand is uniformly distributed between 2000 and 2300. Each calendar costs $17.90 and sells for $25.96, and unsold calendars usually sell out at a 1/2 price sale in January. Assume Joseph can only order in quantities of 50.

a. Write out the algebraic formula for profit as a function of both order quantity (Q) and demand (D).
b. What probability distribution will you use to model the random demand?
c. What is the optimal number to order to maximize Joseph's expected profit? What is the expected profit?
Prepare a summary table of your Crystal Ball results (i.e., # ordered with its expected [or average] profit for all the order quantities you try).