$2.$ Foster Drugs, Inc., handles a variety of health and beauty products. A particular hair

conditioner product costs Foster Drugs $$2\mathrm{.}95$ per unit. The annual holding cost rate is

$20\%$ of the product value. A fixed quantity model recommends an order quantity of

$300$ units per order.

a$.$ Lead time is one day. The product daily demand is normally distributed with a mean

of $150$ units and a standard deviation of $40$ units. What is the reorder point if the firm is

willing to tolerate a $1\%$ chance of stockout?

b$.$ What safety stock and annual safety stock cost are associated with your

recommendation in part $($a$)?$

c$.$ The fixed$-$quantity model requires a continuous$-$review system. Management is

considering making a transition to a fixed$-$period system in an attempt to coordinate

ordering for many of its products. The proposed review time is $4$ days and the lead

time is still one day. The daily demand for the particular hair conditioner product is

normally distributed with a mean of $150$ units and a standard deviation of $40$ units.

What is the recommended target inventory level for this fixed period system if the firm

is willing to tolerate the same $1\%$ chance of stockout associated with any

replenishment decision?

d$.$ What safety stock and annual safety stock cost are associated with your

recommendation in part $($c$)?$

e$.$ Compare your answers to parts $($b$)$ and $($d$).$ The company is seriously considering the

fixed$-$period system. Would you support the decision? Explain.

f$.$ Would you tend to favor the Fixed Quantity system for more expensive items? For

example, assume that the product in the above example sold for $$295$ per unit. Explain.