A large hotel serves banquets and several restaurants from a central kitchen in which labor is shifted among various stations and jobs. Dessert consumption is vir- tually constant and known to be 30,000 desserts a year. Desserts can be produced at a rate of 125 a day, and the hotel is open 365 days a year. It costs \($4.00\) to set up the dessert preparation station, regardless of how many desserts are then prepared, and each dessert costs \($0.40\). The appropriate annual holding cost of a dessert is esti- mated at 300% of the cost of the dessert, due to the risk of spoilage. Unfortunately, the refrigerated pantry that the kitchen uses to store desserts only stores a maximum of 300 desserts, so the kitchen always makes a batch of 300 desserts every time it needs new desserts.

a. How much does the hotel central kitchen pay in total annual holding and order- ing costs on dessert? How often does it produce desserts under its current policy?

b. What is the order size, or run size, that would minimize the total annual cost of desserts? How much savings could be achieved by using this order size?

c. By how much would the central kitchen have to expand the capacity of the refrig- erated pantry that stores desserts to implement the lowest cost policy?