A. M Mean 1700000 S Std Dev 210000 P Price 4.49 C Cost 1.19 V Salvage value 0.48

Question

A.

M   Mean   1700000      
S   Std Dev   210000      
P   Price   4.49      
C   Cost   1.19      
V   Salvage value   0.48      
Cu   Cost of Underage   3.3   P-C  
Co   Cost of Overage   0.71   C-V  
Cr   Cu/(Cu+Co)   0.8229   Optimal Service level  
So   P value   0.8229       Ans A
Demand   1894593.901      
B.

P   Demand   Profit
0.1   1.430874   4.721885
0.2   1.52326   5.026756
0.3   1.589876   5.24659
0.4   1.646797   5.43443
0.5   1.7   5.61
0.6   1.753203   5.78557
0.7   1.810124   5.97341
0.8   1.87674   6.193244
0.81   1.884358   6.218382
0.82   1.892227   6.244348
0.83   1.900375   6.266226
0.84   1.908836   6.287049
0.85   1.917651   6.309038
0.86   1.926867   6.332351
0.87   1.936542   6.357178
0.88   1.946747   6.383755
0.89   1.957571   6.412373
0.9   1.969126   6.443405
0.95   2.045419   6.659673
0.96   2.067644   6.725915
0.97   2.094967   6.808979
0.98   2.131287   6.921737
0.99   2.188533   7.103548

Explanation / Answer

QUESTION 25 (10 points) -Single-Period Inventory Model-Normal Distribution A national pharmacy chain considers selling Christmas cards. These cards are typically released in October and need to be sold before end of December for full value. After December, the remaining cards would be marked down to get sold. For each card, the item cost is $1.19, the selling price from October to December is $4.99, and marked down price after December is 0.48. The pharmacy's historical demand is normally distributed with a mean of 1.7 million cards and a standard deviation of 0.21 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 beloww (a)[3] 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)[1] What is the expected profit? (in millions of dollars with 5 decimals) (f)[1] What is the in-stock probaty?(5 decimals) (g)(1] What is the stockout probability? (5 decimals) Hint: Use the following tables to find the z-value and the corresponding (z) value 0.54767 0.63193 0.71619 0.84257 0.88470 z=NORM.S.INV(av) | 0.11978 | 0.33697 | 0.57155 | 1.00509 | 1.19882 0.80407 0.92342 1.00509 1.08760 1.15585 1.21723 1.30662 1.35151 1.50764 1.53644 2V 2V

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