The Collins Quarter Restaurant in Savannah, Georgia, is apopular place for weekend brunch.

The restaurant serves real maple syrup with French toast andpancakes. The restaurant manager,

Bob, buys the maple syrup from a company in Maine that requires3 weeks for delivery. The

syrup costs Bobbi $4 a bottle and may be purchased in anyquantity. Fixed costs of ordering

amount to about $75 for bookkeeping expenses, and holding costsare based on 20% annual

rate. Based on past experience, the weekly demand for the syrupis normal with mean 12 and

variance 16 (in bottles). Assume that there are 52 weeks in ayear and that all excess demand is

backordered.

(a) (5 points) What is the expected demand and variance duringlead time?

(b) (10 points) What inventory policy should Bob use if a Type Iservice level of 95% is desired

and demand is normally distributed?

(c) (10 points) What inventory policy should Bob use if a TypeII service level of 95% is desired

and demand is normally distributed?

(d) (5 points) What is the expected number of backordered unitsunder Type I and Type II

service levels?

(e) (10 points) Suppose that Bob’s supplier requires a minimumorder size of 500 bottles. Find

the reorder level that Bob should use if he wishes to satisfytype II service level of 99%

assuming normal distribution for the demand.