$(5$ Points$)$ Korner Hardware manager Emerson Jones is interested in determining how

many nativity scenes to order for the $10-$day holiday season. Past experience indicates

that demand for these nativity scenes averages $8$ per day during this $10-$day period, with

a standard deviation of $2$ per day. Demand is approximately normal. Emerson purchases

the nativity scenes for $$15$ per unit and sells them for $$30$ each during the season. After

Christmas, they are marked down as sale items for $$10$ each. How many should

Emerson order for the coming holiday season?

Note: Demand per day has mean of $8$ and standard deviation of $2.$ This is equivalent to

say, demand in this ten$-$day period is approximately normal with mean of $80$ and

standard deviation $2\sqrt[\phantom{2}]{?}10.$

a$.(2$ Points$)$ What is the cost of overstock? And what is the cost of stockout?

b$.(1$ Point$)$ What is the critical ratio?

c$.(1$ Point$)$ What is the associated $z-$value? $($z$-$value table is attached at the end of

this homework$)?$

d$.(1$ Point$)$ What is the optimal order quantity?