A perishable dairy product is ordered daily at a particular supermarket. The product,

which costs $$1\mathrm{.}19$ per unit, sells for $$1\mathrm{.}65$ per unit. If units are unsold at the end of the day, the supplier takes them back at a rebate of $$1$ per unit. Assume that daily demand is

approximately normally distributed with m $\_150$ and $\backslash$sigma $\_30.$

a$.$ What is your recommended daily order quantity for the supermarket?

b$.$ What is the probability that the supermarket will sell all the units it orders?

c$.$ In problems such as these, why would the supplier offer a rebate as high as $$1?$ For

example, why not offer a nominal rebate of$,$ say, $25$ per unit? What happens to the

supermarket order quantity as the rebate is reduced?