The 4N Company reacts to shortages at a particular branch warehouse in the following fashion: Any shortage is effectively eliminated by bringing material in from the plant by air freight at a cost of $2.50/kg. Assume that the average demand rate of an item is essentially constant with time and that forecast errors are normally distributed. Assume that an

(s, Q) system is to be used and that Q, if needed, is prespecified. To answer the following questions, introduce whatever symbols are necessary:

a. What are the expected shortage costs per cycle?

b. What are the expected shortage costs per year?

c. What are the expected total relevant costs per year associated with the safety factor k?

d. Develop an equation that the best k must satisfy.

e. If we had two items with all characteristics identical except that item 1 weighed more

(on a unit basis) than item 2, how do you intuitively think that the two safety factors would compare? Verify this using the result of part (d).