(The first sub-question is worth 3 points and the second sub-question is a bonus question worth 1 additional point.)

Consider a store that sells newspapers. The store owner must order the newspapers in the early morning and sell them during the day. The owner pays his supplier 30 cents a copy and sells the paper to his customers for 50 cents a copy. The owner estimates that the daily demand for the newspaper at his store is a normal distribution of a mean of 100 and a standard deviation of 25. The following two sub-questions (a)-(b) are independent of one another.

(a) Suppose that any unsold copies will be thrown away by the store at the end of the day. What is his optimal order quantity in the early morning? What is the corresponding probability of stockout?

(b) (bonus question) Suppose that the store owner has now negotiated with the supplier such that any unsold copies at the end of the day can be returned to the supplier, and the owner gets 25 cents back from the supplier for each returned copy. However, the supplier also demands that the owner shares 10 cents of the profit for each sold copy during the day. What is the optimal order quantity for the store owner in the early morning?