2023 Problem 1 A Your firm uses a fixed order quantity system and operates 52 weeks

Problem 1:

A. Your firm uses a fixed order quantity system and operates 52 weeks per year. One of the items handled has the following characteristics 
Annual Demand = 20,000 units 
Order Cost = $ 40 per order 
Holding Cost = $ 2 per unit per year 
Lead time = 2 weeks 
Demand is normally distributed with a standard deviation of weekly demand of 100 units. 
a) Calculate the item’s EOQ. What is the average time between orders (in weeks) 
b) Find the safety stock and reorder point that provide a 95% customer service level 

B. The University Bookstore at a prestigious private university buys mechanical pencils from a wholesaler. The wholesaler. The wholesaler offers discounts for large according to the following price schedule: 
Order Quantity Price per Unit 
0 – 200 $ 4.00 
201 – 2,000 $ 3.50 
2,001 or more $ 3.25 

Problem 2:
A. A textile manufacturer wants to set up a control chart for irregularities (.e.g. oil stains, shop soil, loose threads, and tears) per 100 square yards of carpet. The following data were collected from a sample of twenty 100-square-yard pieces of carpet 
Sample # 1 2 3 4 5 6 7 8 9 10 
Irregularities 11 8 9 12 4 16 5 8 17 10 
Sample # 11 12 13 14 15 16 17 18 19 20 
Irregularities 11 5 7 12 13 8 19 11 9 10 

Using the above data, set up the appropriate control chart using 3-sigma limits and determine if the process is in control. Also plot the chart

B.Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed below. Using the factors A2, D3 and D4, determine upper and lower control limits for mean and range charts, and decide if the process is in control. Draw the X-bar chart and R-chart also in order to illustrate your conclusions 

Sample # 
1 2 3 4 5 6 
79.2 80.5 79.6 78.9 80.5 79.7 
78.8 78.7 79.6 79.4 79.6 80.6 
80.0 81.0 80.4 79.7 80.4 80.5 
78.4 80.4 80.3 79.4 80.8 80.0 
81.0 80.1 80.8 80.6 78.8 81.1