A chemical company produces sodium bisulfate. The company uses a particular raw material for production. This raw material is ordered from an external supplier, and it has a 9 days lead time. The consumption of the raw material in the production process is approximately normally distributed with a mean of 20 tons per day and a standard deviation of 7 tons per day. Each ton of the raw material costs the company S400. The fixed cost of replenishment is $500 per order, and holding costs are based on a 25% annual interest rate. The company wants to be able to satisfy 98% of its demand. The company is working 365 days a year. (a) What is the optimal lot size (order quantity) and reorder level? Hints: • Round Q and R to the nearest integer. • Represent n(R) and L(z0) in 3 decimal places (*.***) • Represent z in 2 decimal places (*.**) Iteration n(R) L(z0) R 1 2 For Blank 6 (b) Based on the answer in part (a), what is the expected number of stock-outs per cycle? (Hint: use 1 decimal place (*.*) (c) What are the average annual holding and setup costs?

A chemical company produces sodium bisulfate. The company uses a particular raw material for production. This raw material is ordered from an external supplier, and it has a 9 days lead time. The consumption of the raw material in the production process is approximately normally distributed with a mean of 20 tons per day and a standard deviation of 7 tons per day. Each ton of the raw material costs the company S400. The fixed cost of replenishment is $500 per order, and holding costs are based on a 25% annual interest rate. The company wants to be able to satisfy 98% of its demand. The company is working 365 days a year. (a) What is the optimal lot size (order quantity) and reorder level? Hints: • Round Q and R to the nearest integer. • Represent n(R) and L(z0) in 3 decimal places (*.***) • Represent z in 2 decimal places (*.**) Iteration n(R) L(z0) R 1 2 For Blank 6 (b) Based on the answer in part (a), what is the expected number of stock-outs per cycle? (Hint: use 1 decimal place (.) (c) What are the average annual holding and setup costs?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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