The distribution center of Arcadia supermarkets buys milk buys organic milk in 1-gallon bottles from a supplier in Minnesota at the price of $6.25 per bottle and distributes it to its 50 stores. The total demand of the 50 stores is about 1000 bottles in a week (assume 52 weeks in a year). The demand is steady with no significant variability. Order setup cost of the supplier in Michigan is $200 and is independent of the order size. The supplier has the order lead time of 2 days. The inventory carrying rate at DC is 36 percent, of which 10 percent is the opportunity cost of money and 26 percent is the warehousing costs.

1. Calculate the optimal order quantity according to the basic EOQ model Arcadia realizes that their cost of capital is charged compound interest.

2. They want to change their optimal order quantity for the EOQ model with compound interest. What is the optimal order quantity if the compound interest model is used?

3.What is the penalty in terms of annual total cost if they dont use the compound interest model to calculate their optimal order quantity (and instead, they use the basic EOQ model)?

Consider the supermarket chain in Problem 1. They realize that there is deterioration in their milk inventory and that they need to consider this deterioration in their model. The instantaneous deterioration rate is 20 gallons per year, which corresponds to an average life of 1/20=0.05 year per gallon = 18.25 days per gallon of milk.

4.Calculate the optimal order quantity according to the deterioration based model.

5.What is the penalty in terms of annual total cost if they dont use the deteriorating items inventory model with compound interest to calculate their optimal order quantity (and instead, they use the basic EOQ model)?