A perishable diary product is ordered daily at a particular supermarket. The product, which cost $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 normal distributed with μ = 150 and σ = 30. 1. What is your recommended daily order quantity for the supermarket? 2. What is the probability that the supermarket will sell all the units it orders? 3. 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?

Question

A perishable diary product is ordered daily at a particular supermarket.  The product, which cost $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 normal distributed with μ = 150 and σ = 30.  1.  What is your recommended daily order quantity for the supermarket?  2.  What is the probability that the supermarket will sell all the units it orders?  3.  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?