Pat sells Sunday papers outside a retirement home on Sunday mornings. Demand for Sunday papers is Normally distributed with mean 50, standard deviation 15. Pat collects $2.5 per paper and pays $1 for a paper. The retirement home residents think fondly of Pat and aren’t too upset when papers run out. On the other hand, any papers Pat is left with are thrown into the recycling bin. Pat is trying to figure out a systematic ordering policy. When Pat runs out of papers, the sale is lost.
1. Newsvendor Quantity: How many Sunday papers should Pat stock to maximize expected profit? Show your work.
2. Newsvendor Quantity with Alternative Source: For this part of the question only, when Pat runs out of a paper (s)he procures it from town at $1.75 per paper. Calculate the in-stock probability corresponding to the new number of Sunday newspapers stocked initially to maximize expected profit.
3. (i) What role does the statement “The retirement home residents think fondly of Pat and aren’t too upset when papers run out” play in your calculations above and what might change if this statement were not true? Also, if Pat stocks 40 Sunday papers, how many retirement home residents’ demand would not be satisfied on average?
(ii) If Pat stocks 40 Sunday papers, what is the chance that his/her corresponding actual realized profit exceeds 47.5$ on a Sunday morning? Note: Actual realized profit is not the expected profit, it is the profit resulting from a specific demand value that materializes from among the set of possible demand values. For instance, if the Pat’s demand on Sunday is 30 papers, then his/her corresponding profit with 40 papers stocked is 30*(2.5-1)-10*1 = 35$.