A dairy product is ordered daily at a particular supermarket. The product, which costs $1.19 per unit, sells for $1.65 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 a mean of 150 and a standard deviation of 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 cents per unit? What happens to the supermarket order quantity as the rebate is reduced?