Jennifer's Donut House serves a large variety of doughnuts, one of which is a blueberry-filled, chocolate-covered, supersized doughnut supreme with sprinkles. This is an extra large doughnut that is meant to be shared by a whole family. Since the dough requires so long to rise, preparation of these doughnuts begins at 4:00 in the morning, so a decision on how many to prepare must be made long before learning how many will be needed. The cost of the ingredients and labor required to prepare each of these doughnuts is $1. Their sale price is $3 each. Any not sold that day are sold to a local discount grocery store for $0.50. Over the last several weeks, the number of these doughnuts sold for $3 each day has been tracked. These data are summarized next.

(a) What is the unit cost of underordering? The unit cost of overordering?

(b) Use Bayes'decision rule presented in Sec. 15.2 to determine how many of these doughnuts should be prepared each day to minimize the average daily cost of underordering or overordering.

(c) After plotting the cumulative distribution function of demand, apply the stochastic single-period model for perishable products graphically to determine how many of these doughnuts to prepare each day.

(d) Given the answer in part (c), what will be the probability of running short of these doughnuts on any given day?

(e) Some families make a special trip to the Donut House just to buy this special doughnut. Therefore, Jennifer thinks that the cost when they run short might be greater than just the lost profit. In particular, there may be a cost for lost customer goodwill each time a customer orders this doughnut but none are available. How high would this cost have to be before they should prepare one more of these doughnuts each day than was found in part (c)?