A local convenient store sells an evening paper, the Evening News. The owner of the store pays his supplier 30 cents a copy and sells the paper to his customers for 50 cents a copy. He estimates that the demand for the Evening News at his store is a normal distribution of mean 100 and standard deviation

The following three sub questions are independent from 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 before knowing the actual demand?

(b) Suppose that the store owner has now negotiated with the supplier such that any unsold copies can be returned to the supplier, and he gets 25 cents back. However, the supplier also demands that he shares 5 cents of his profit for each sold copy. Under this new contract, what is the optimal order quantity for the store owner?

(c) Suppose that the store owner found another supply source of the same newspaper. Now, in addition to the newspapers he can buy from the original supplier at 30 cents each before demand is known, the owner can also buy an unlimited quantity of additional newspapers from the new supplier at 45 cents each after demand is known. What is the store owner's optimal order quantity now from his original supplier? Suppose that any unsold copies will be thrown away by the store at the end of the day.