Problem 4. (Deterministic Inventory Model. Total 15 pts.) David's Delicatessen sells a special Hebrew sausage. The owner, David Gold, estimates that the demand for the sausage is steady at 500 kilograms a week. The special sausage cost Gold $6.00 a kilogram. The cost of ordering and shipping from the supplier is $300 each order. Gold's accountant, Irving Wu, estimated an annual holding cost of the sausage is 15% of the sausage purchase cost.

a) How many kilograms of the special sausage should Goldorder each time to minimize the annual costs on holding and ordering? Calculate the annual total costs of holding, ordering, and purchasing the sausage.

b) What is the maximal inventory level, average inventory level? How many times will Mr. Gold order each year?

c) At what inventory level should Mr. Gold reorder, assumingthat it will take two weeks to receive an order?

d) Assume a dedicated truck will be used for shipping each order. The shipping company has two different size trucks, say, large trucks and small trucks, to be used todeliver the ordered product. i)Large truck: each truck can deliver a maximum load of 5000lb at a cost of $400; ii)Small truck: each truck can deliver a maximum load of 3000lb at a cost of $300.

If the order size exceeds to the capacity of one truck we use, an additional truck (with an additional truck cost) will be used. Use Quantitative analysis to determine theorder size and the type of truck be used for shipping the orders that will minimize the total costs.