1. This file contains 20 samples collected from a cosmetic manufacturing line. The data indicates the skin sensitivity level to a har color. The Excel file also has theA2,D3,D4, andd2table on the second sheet. Please write"see attachment"in the answer space if you do graphics in Excel file and you want to attach it to your homework. Please try to use Excel, otherwise you may have to do a lot of computation by hand.

(a)Construct an X-bar chart for this manufacturing line:

X-bar Chart i.Is this process"in control"?ii.Do you notice any problems despite your answer to Part i?

___________________________________________________________________________ ___________________________________________________________________________(b)Construct an R-Chart for this manufacturing line:

R-Chart

i.Is this process"in control"?ii.Based on your calculation for the X-Bar Chart and R-Chart, compare your answers regarding the "in control" question? Do the charts result differently? Why or Why Not?

___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

2.You have been the inventory manager at Malmart Distribution Center. You have estimated that the annual demand for passenger car tires is 200,000 units. Placing an order costs $300. Cost to hold a tire is $3 per year. Cost per tire is $70.

(a)How much (Q*) and how often do you need to order and fulfill the demand?

Q*: _________T*: _________

(b) At the end of your first year of managing, you realize that the demand is variable. However, the average annual demand is still 200,000 with a standard deviation of 5.6 tires per day. The tires supplier cannot deliver the products on the same day. The average lead time is now 20 days with a standard deviation of 4.1 days. You consider a 95% Service Level to satisfy customers. What is the Reorder Point (ROP)?

ROP: _________

(c) You also want to test OUT model. The review process,T, is 30 days. Assume that the on- hand inventory is 15,000 tires. What is the OUT inventory level and the Order Quantity (Q)? (Hint: Use the information in Part b to find the value for the remaining parameters.)

OUT: _________Q: _________

Data table:

Sample	x1	x2	x3	x4	x5	x6	X-bar	Range
1	13.2471	13.9760	13.6090	13.8000	14.4900	13.2319
2	13.8440	13.2529	13.2127	13.2859	13.2421	13.2336
3	13.2153	13.2155	13.2349	13.2619	13.2297	13.2753
4	12.2240	13.2419	12.0240	12.0400	13.2827	13.2635
5	13.2051	13.2235	13.2489	13.2537	13.2381	13.2216
6	13.2649	13.2023	13.2735	13.2229	10.4446	13.2138
7	13.2367	13.2443	13.2267	13.2399	13.2137	10.2223
8	13.2277	11.6364	13.2799	10.4463	13.2101	13.1989
9	12.5821	12.5793	10.4468	10.8468	10.3682	12.6125
10	11.1100	12.7393	10.4690	13.4457	10.4904	14.0022
11	14.2339	10.4705	14.0704	10.8846	10.4865	11.6468
12	12.4513	13.1163	13.4088	10.9046	12.1947	13.4720
13	13.5483	10.3046	10.4865	12.6323	13.8351	13.9566
14	13.7246	10.4684	13.9760	5.9980	13.9805	13.4641
15	12.7869	10.8840	12.9795	12.9885	12.5297	14.4680
16	13.0564	13.3829	13.1568	12.2786	8.8885	13.6612
17	10.2469	14.4000	8.8846	12.5025	12.8000	6.4440
18	12.5965	8.8888	13.2913	8.4905	12.0733	14.0240
19	11.5467	12.7803	11.6699	8.8880	13.0085	13.8722
20	13.5980	8.4640	13.6852	14.7798	12.0635	4.9000