QUESTION 24 (10 points) - Single-Period Inventory Model - Normal Distribution A national pharmacy chain considers selling graduation cards this year. These cards are typically released in February and need to be sold before the end of May. After May, the remaining cards would be marked down to get sold. For each card, the item cost is $0.91, the regular selling price by the end of May is $4.99, and the marked down price after May is $0.48. The pharmacy's historical demand is normally distributed with a mean of 1.82 million cards and a standard deviation of 0.16 million cards. You would need to show equations, steps, and the final results with units for full credits. Answers are in millions using 5 decimals, e.g. 1.76384 million cards. You should not round up the numbers! For simplicity, all taxes and other costs are not considered. All parts below are based on the optimal order quantity decision in part (a). See Hint below. (a)[2] To maximize expected profit, how many cards should the pharmacy carry this year? (b)[2] Sketch the normal demand distribution with details to illustrate the business decision. (c)[1] What is the expected inventory? (in millions with 5 decimals) (d)[1] What are the expected sales? (in millions with 5 decimals) (e)[2] What is the expected profit? (in millions of dollars with 5 decimals) (f)[1] What is the in-stock probability? (5 decimals) (g)[1] What is the stockout probability? (5 decimals) Hint: Use the following tables to find the z-value and the corresponding I(z) value. av 0.58803 0.67849 0.76896 0.90466 0.94989 zx = NORM.S.INV(av) 0.22247 0.46349 0.73542 1.30855 1.64378 zx 1.04684 1.30855 1.50483 1.70112 1.96283 I(zv) 1.12299 1.35326 1.53382 1.71935 1.97220 0.58803 0.67849 0.76896 0.90466 0.94989 Z=NORM.S.INV(av) 0.22247 0.46349 0.73542 1.30855 1.64378 zv I(zy) 1.04684 1.12299 1.30855 1.35326 1.50483 1.53382 1.70112 1.71935 1.96283 1.972201