Question $4(15$ points$)$: Newsvendor Model

A retail outlet sells a perishable product for $$13$ per unit. The cost of the product is $$6$

per unit. The product not sold has the salvage value of $$2.$

a$)$ Compute the overage cost and underage cost per unit.

b$)$ If the demand follows the normal distribution with an average of $350,$ and the

standard deviation of $110.$ What is the optimal order quantity to maximize the

expected profit?

c$)$ What is the optimal ordering quantity if the retailer uses the following discrete

distribution for demand?

quantity $100150200250300350400450500$

probability $0\mathrm{.}050\mathrm{.}050\mathrm{.}150\mathrm{.}150\mathrm{.}200\mathrm{.}150\mathrm{.}150\mathrm{.}050\mathrm{.}05$