19 Apr Problem 2 (Week 15; Bayes Rule to evaluate Product / Operations Reliability) ?? Suppose that ?It is known that factory X supplies 60% of the total
Problem 2 (Week 15; Bayes Rule to evaluate Product / Operations Reliability)
Suppose that It is known that factory X supplies 60% of the total bulbs available and Y supplies 40% of the total bulbs available.
1)What is the chance that a purchased bulb will work forever?
2)Given that a purchased bulb will work forever, what is the chance that it was made in Factory X?
Kishore K. Pochampally
Name:_____________________
Final Exam (take-home)
· There are 2 problems based on the following concepts/problems we covered in class. Each problem is worth 50 points.
|
Week # |
Topic |
|
14 |
Operations Simulation |
|
15 |
Bayes Rule to evaluate Product / Operations Reliability |
· This Word file (with your solutions) is due at the ‘Final Exam (take-home)’ assignment on Brightspace by 11:59 PM on Apr 19 (Tues).
· Group work is prohibited.
· Since the Final Exam is take-home, there will not be a lecture on Apr 19 (Tues).
Problem 1 (Week 14; Operations Simulation)
Under the new policy at a truck dealership, two trucks are to be ordered whenever the number of trucks on hand is four or fewer . Orders can be filled overnight. According to the dealer’s records, the relative frequency distribution for daily demand is:
|
Demand |
Relative Frequency |
|
0 |
0.10 |
|
1 |
0.45 |
|
2 |
0.45 |
The manager has hired you as a consultant and wants you to simulate his inventory level for 8 days . He has told you to assume a beginning inventory of 9 trucks .
Solution
|
Demand |
Relative Frequency |
Random Numbers |
|
0 |
0.10 |
|
|
1 |
0.45 |
|
|
2 |
0.45 |
Table of Random Numbers
|
00 |
01 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
09 |
|
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
|
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
|
30 |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
|
40 |
41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
|
50 |
51 |
52 |
53 |
54 |
55 |
56 |
57 |
58 |
59 |
|
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
69 |
|
70 |
71 |
72 |
73 |
74 |
75 |
76 |
77 |
78 |
79 |
|
80 |
81 |
82 |
83 |
84 |
85 |
86 |
87 |
88 |
89 |
|
90 |
91 |
92 |
93 |
94 |
95 |
96 |
97 |
98 |
99 |
|
Day |
Random Number |
Demand |
Beginning Inventory |
Ending Inventory |
|||||
|
1 |
31 |
||||||||
|
2 |
73 |
||||||||
|
3 |
10 |
||||||||
|
4 |
15 |
||||||||
|
5 |
37 |
||||||||
|
6 |
82 |
||||||||
|
7 |
19 |
||||||||
|
8 |
24 |
Problem 2 (Week 15; Bayes Rule to evaluate Product / Operations Reliability)
Suppose that two factories supply light bulbs to the market. Factory X's bulbs work forever in 99% of cases, whereas factory Y's bulbs work forever in 95% of cases. It is known that factory X supplies 60% of the total bulbs available and Y supplies 40% of the total bulbs available.
a) What is the chance that a purchased bulb will work forever?
b) Given that a purchased bulb will work forever, what is the chance that it was made in Factory X?
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