Problem 1:Problem # 1 illustrates the logic of the ‘’The Newsvendor Problem”.The Newsvendor problem enables us to identify the optimal stocking quantity for a perishable product with an unpredictable demand., and a single stocking decision made prior to observing any demand (i.e., no replishment).Using the simulation in the spreadsheet Hamptonshire Express # 1, we observe the relationship between the stocking quantity and Sheen’s profits.[pic 1][pic 2][pic 3][pic 4][pic 5][pic 6][pic 7][pic 8][pic 9][pic 10][pic 11][pic 12][pic 13][pic 14][pic 15][pic 16][pic 17][pic 18][pic 19][pic 20][pic 21][pic 22][pic 23][pic 24][pic 25][pic 26][pic 27][pic 28][pic 29][pic 30][pic 31][pic 32][pic 33][pic 34][pic 35][pic 36][pic 37][pic 38][pic 39][pic 40][pic 41][pic 42][pic 43][pic 44][pic 45]First notice the optimal stocking quantity ( 584units ) is not equal to the mean demand of 500, because the cost of overstocking is not equal to the cost of understocking.In problem # 1, the understocking cost is equal to $0.80($1-0.20) per unit of unmet demand , while the overstocking cost is only $0.20 per newspaper.We can also see that the fill rate ( the expected fraction of demand that Sheen can satisfy from inventory) increases as Sheen stocks more newspapers .However the fill rate increases more slowly at higher levels of Q-while the first 100 units of stock increase the fill rate from 0% to 21%, increasing the stocking quantity ffrom 500 to 600 the fill rate by only approximately 6% ( from 93% to 99%).Sheen is less likely to sell the marginal stocking quantity at higher values of Q, and hence , these units are less likely to increase her fill rate.Sheen’s profit increases from a loss of $40/day (when the stocking quantity is 0) to $332/day (when Sheen stocks 584 newspapers).The profit declines to $259(when Sheen stocks 1000 units, at the beginning of each day).This pattern is consistent withe the newsvendor model. At low levels of Q (i.e. close to 0) , Sheen sells few newspapers (i.e. loses sales )due to inadequate inventory and thus has low profit.Additional units increase Sheen’s expected sales , but also lead to more unsold inventoy,and thus higher overstocking costs.To identify optimal stocking quantity , Sheen has to trade-off the expected understocking cost , against the expected the overstocking cost.Since the cost of understocking ($0.80 per unit ) is more than the cost of overstocking ($0.20 per unit ), the profit function is maximized at a stocking quantity (584 units) that exceeds the mean.