-Production Rate 1,000 dozen pies every 20 minutes
-Monthly Production – 60,000 dozen pies
-Yearly production - 720,000 dozen pies
- Thrift store demand – 240 dozens per month
-Thrift store storage max - 1000 dozen pies
-Rejected batches are first sold at the Thrift Store and excess donated to charity -The threat of situation similar to energy crisis period is minimal and fines for substantially underweight pie is nonexistent -Five samples taken from QC during manufacturing are independent
What is the potential risk for the company if the fill target lowered to 8.22 oz per pie? What are the actions should you recommend to Mr. Jenkins?
Fill target 8.44 oz. Five Samples taken from every batch of 1,000. (Please find conversion table of the sampling and averages on Appendix 1) Advantages:
Based on the current fill target more than 95.45% of packages are with weight above 8oz and probability of package to be underweight is less than 0.0063 % (more than 4 STD from the mean) z=(8-8.49)/STD/SQRT/(5) Potential fine for underweight package is practically nonexistent. (We apply the Central Limit Theorem) Disadvantages:
Based on the higher fill target every pie is filled with additional 0.22oz of macaroni and cheese, which add a significant cost. The annual impact is 0.22oz* 60,000*12 (dozens)*12(months) = 1,900,800 oz. The cost is 1,900,800*1.82/8.44= $ 409,888.15. This is a significant opportunity for savings given the current no energy crisis and.
Change of the fill target to 8.22 oz.
– Savings of $ 409,888 which is a considerably high amount
-Probability that a batch of 1,000 will be lower than 8 oz will be: z=(x-m)/STD/SQRT (5) or (8-8.22)/0.22/SQRT (5)=-2.24
If z=-2.24 p=0.0125 or probability of a batch to be less than 8oz is 1, 25%. This could give an annual impact of 9,000 dozens or 108,000 pies. As the FDA charge is $ 15 for an underweight batch less than 7.50 oz...