3. Kroger lnc. (40 points) Kroger at Scottsville Road makes fresh pumpkin pies e

Question

3. Kroger lnc. (40 points) Kroger at Scottsville Road makes fresh pumpkin pies each morning. The daily demand for these pies is a random variable with a distribution estimated from manager Mike's experience given by Number of pumpkin pies sold in one da Probability 10 15 20 25 30 35 0.10 0.15 0.25 0.10 0.25 0.05 0.05 0.05 Mike knows that the cost of making one pumpkin pie is about $10. In the store, pumpkin pies are sold for $17.50 each. At the end of the day, unsold pumpkin pies are sold to Bowling Green food bank for $8.50 each. (a) How many pumpkin pies should Kroger make at the start of each day? (b) Determine the average number of pumpkin pies sold to Bowling Green food bank (Average Overstock) and average number of customers turned away (Average Understock)

Explanation / Answer

No of Sales Prob Cumm Prob P Price 17.5 0 0.1 0.1 C Cost 10 5 0.15 0.25 V Salvage value 8.5 10 0.25 0.5 Cu Cost of Underage 7.5 P-C 15 0.1 0.6 Co Cost of Overage 1.5 C-V 20 0.25 0.85 Cr Cu/(Cu+Co) 0.833333 25 0.05 0.9 So no of sales 20 Ans A 30 0.05 0.95 Prob 0.85 35 0.05 1 P o P overstock 0.016667 P understock 0.15 Cost overstock 0.025 Cost understock 1.125 (5*.05+10*.05+15*.05) Units understock 1.5 Ans B Po*20 Units overstock 0.333333 Ans B

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