Question $1$

Demand for disposable masks skyrocketed in March $2020$ when quarantine mandates first took effect. At the time, retailers could only place a single order to

cover demands through the end of the summer.

A certain retailer purchased disposal masks from a supplier at a cost of $$20$ per box, and sold them for $$30$ per box. By the end of summer, demand for masks

subsided considerably and all masks that weren't sold during the summer could be sold at a discounted price of $$18$ per box. The retailer estimated that

demand between March and August would be normally distributed with $=10,000$ and $=1525$ boxes.

$($a$)$ If the retailer orders $Q=10,800$ boxes of masks in March, what would be the service level? $(10$pts$)$

$($b$)$ If the retailer orders $Q=10,800$ boxes of masks in March, what would be the expected profit? Express your answer in currency format. $(6$pts$)$

$($c$)$ If the retailer wants the probability of stockout to be $5\%,$ how many boxes should be ordered in March? Round final answer to a whole number. $(6$pts$)$

$($d$)$ What is the optimal stockout probability? $(2$pts$)$

$($e$)$ How many boxes should be ordered in March in order to achieve the optimal service level? Round final answer to a whole number. $(6$pts$)$

$($f$)($This one is a little tricky $...$ maybe save for later$)$ The sales department doesn't like stockouts because they are the ones who have to deal with unhappy

customers. The sales staff is well trained and pretty good at placating customers when shortages occur, but they aren't perfect. They sometimes lose

customers and estimate the value of a lost customer as $$4\mathrm{.}67$ per box of unsatisfied demand. What would be the optimal service level when this loss of

customer goodwill cost is taken into account? $(7$pts$)$