# Amore Frozen Foods

Topics: Arithmetic mean, Central limit theorem, Probability theory Pages: 2 (639 words) Published: September 30, 2008
Assumptions:

-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

Questions:
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?

Current situation:
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

Risk
-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...