The San Diego County Fair takes place annually from the first week of June through July 4. Every year, the fair hosts nearly a hundred stands that sell various food and drink items, and provides dozens of areas throughout the fairgrounds specifically designated for eating. As the fairgrounds are situated very close to the ocean, evenings at the fair can be quite chilly. After years of fielding complaints from guests about the dining areas being too cold in the later hours of the day, management has decided to place heat lamps throughout each dining area. The lamps will be powered by reusable propane tanks which are to be provided by a local propane supplier. As this is the first year lamps will be provided, management is still refining its plan for propane delivery. The supplier has suggested a delivery process in which it would deliver a certain number of filled tanks every day over a fixed number of days. At the end of this production run, the supplier would collectall empty tanks and return them to its warehouse to be refilled. The fair would then deplete its supply of propane until the next production run, at which point the supplier will deliver the refilled tanks and again collect the empty ones for refilling. This cycle would repeat through the duration of the fair, which runs every day for 5 weeks (35 days total). Management has negotiated to buy the filled tanks at $12 per tank, and the supplier has negotiated a fixed delivery rate of $100 per production run. The supplier has the capacity to deliver up to 300 tanks per day. As the lamps are to be lit on a consistent daily schedule, management estimates that propane will be consumed at a near constant rate of 90 tanks each day. Management also assumes that the holding costs for filled propane tanks total approximately $2.50 per tank. (As empty tanks do not require careful storage, management has decided to attribute holding costs only to any filled tanks on the premises.)

a. What is the optimal number of tanks that should be delivered in each complete production run in order to minimize the total cost of managing inventory? Note that any ‘annual’ estimates used in your calculations should only reflect the duration of the fair. (3 pts)

b. Using the optimal lot size, how long will each production run last? (1 pt)

c. Although the fair plans to accommodate a supply of both filled and empty tanks at any given moment, the filled tanks require special care, as they are both pressurized and highly flammable, and must be stored in a safe environment until ready for use. In order to plan for storage accordingly, management would like to know the following: using the recommended order quantity as determined in the part A, what is the maximum number of filled propane tanks that will be on the premises at any given moment? (1 pt)

d. How many production runs will occur over the length of the fair? (1 pt)e. What is the total cost of managing inventory? (excluding cost of goods) (2 pts)