Every day Mr. Rogers has his newspaper delivered by Tommy, his next door neighbor. Tommy also sells newspapers on the corner in Mr. Rogers' neighborhood and he asked Mr. Rogers for some help in figuring out how many to order. As you know, newspapers are daily items with uncertain demand and no opportunity to backorder. Once you miss an opportunity to sell a paper, that reader may never come back. Tommy buys the newspapers for $0.50 and sells them for $1.75. At the end of the day, Tommy can sell his leftover inventory back to the publisher for $0.40. The question is how many papers should Tommy buy? To begin your analysis you decide to look at a discrete demand distribution. You decide that based on past history it can be predicted to be similar to the table below:

1. What is the cost of underage?

2. What is the cost of overage?

3. given that Tommy orders 350 papers and the demand is 300, what would his profit be?

4. what is the critical fractile