$($Q$2)$ Newsvendor problem version $1$

Jason, an enterprising CB student, decides to operate a news$-$stand selling copies

of the SCMP$.$ Every morning, he buys copies of the newspaper from the publisher

at a cost of $$16$ per copy, and he sells each copy of the newspaper at a retail price

of $$20.$ Any unsold copies are discarded at a loss at the end of the day. Jason was

able to apply what he had learned in the course CB$2200$ Business Statistics,

when he observed that the daily demand for newspapers is approximately

normally distributed with mean $800$ and standard deviation $150.$

A$.$ What is the underage cost, overage cost and critical fractile for the

newsvendor problem faced by Jason?

B$.$ What is the optimal order quantity $q^{**}?$

C$.$ If Jason were to order $q^{**}$ newspapers, what is the probability of a stockout?