$3.$ a$)$ A food processor uses approximately $40,000$ glass jars a month for its fruit juice product. Because of

storage limitations$,$ a lot size of $5,000$ jars has been used. The monthly holding cost is $20$ cents per jar, and reordering cost is $ $90$ per order. The company operates an average of $24$ days a month.

i$)$ What penalty is the company incurring by its present order size?

The manager would prefer ordering $6$ times each month but would have to justify any change in order size. One possibility is to simplify order processing to increase the ordering cost. What ordering cost would enable the manager to justify ordering every four days?

Suppose that after investigating ordering cost, the manager is able to reduce it to $ $75.$ How else could the manager justify using an order size that could be consistent with ordering every four days?

b$)$ Given this information:

Expected demand during lead time $=360$ units

Standard deviation of the lead time demand $=40$ units

Determine each of the following, assuming that lead time demand is distributed normally:

i$)$ The ROP that will provide a risk of stock$-$out of $2\%$ during lead time.

The safety stock needed to attain a $2\%$ risk of stock$-$out during lead time.

iii$)$ Would a stock$-$out risk of $5\%$ require more or less safety stock than a $2\%$ risk? Explain.

Would the ROP be larger, smaller, or unaffected if the acceptable risk were $5\%$ instead of $2\%?$ Explain.