1. Three different time estimates for various activities of a project are given in the below table. Construct a PERT network and find out (a) The earliest possible time (TE) to complete the different activities, (b) The latest allowable time (TL) for them, (c) The slack values, (d) The critical paths, and (e) The probability factor for completing the project in 30 weeks.

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SOLUTION:

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(iv) Critical Path

1–2–4–6–7–9–10 = 28 weeks.

Vcp = 2 and σcp = 1.41

(v) The probability factor for completing the project in 30 weeks.

Z = (X – μ)/σ

where X = 30 weeks, μ = 28 weeks and σCP = 1.41

Hence,

Z = (30 28)/141 = 1.41

Z is the number of standard deviations by which X exceeds μ

μ = Te is the total project duration, and

X = due or scheduled date or time

From the table of Standard Normal Distribution Function, the corresponding percentage probabilities

are given as follows:

For Z = 1.41 the probability is 92.07 % and for Z = 1.42 the probability is 92.22 %.

Therefore, there is 92.13% probability that the project will be finished in 30 weeks.

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Procedures
These are the procedures I have taken in order to find the solution to this problem:
1. Research
I have created a poll for students in high school to take (30 people), and these were the results:
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Yes, they should encourage the student without overwhelming them will all the work
15 People
50%
Yes, but it’s good preparation for college
10 People
30%
No, there isn’t any pressure
5 People
20%
Articles about students that have commit suicide because of so much pressure:
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Poster
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CAPM, beta, and WACC
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Beta risk
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Risk-adjusted discount rate
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Problem 1
The following data were obtained from a project to create a new portable electronic.
Activity Duration Predecessors
A 5 Days ---
B 6 Days ---
C 8 Days ---
D 4 Days A, B
E 3 Days C
F 5 Days D
G 5 Days E, F
H 9 Days D
I 12 Days G
Step 1: Construct a network diagram for the project.
Step 2: Answer the following questions: (15 points total)
a) What is the Scheduled Completion of the Project? (2 points)
32 -> CORRECT
b) What is the Critical Path of the Project? (3 points)
B,D,F,G,I -> CORRECT
2,4,6,7,9
c) What is the ES for Activity D? (2 points)
6 -> Correct
d) What is the LS for Activity G? (2 points)
15
e) What is the EF for Activity B? (2 points)
6 -> Correct
f) What is the LF for Activity H? (2 points)
32 -> Correct
g) What is the float for Activity I? (2 points)
0
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Activity Duration Predecessors
A 6 weeks ---
B 6 weeks ---
C 5 weeks B
D 4 weeks A, C
E 5 weeks B
F 7 weeks D, E, G
G 4 weeks B
H 8 weeks F
I 5 weeks G
J 3 week I
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a) Calculate the scheduled completion time. (3 points)
30
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B,C,D,F,H
c) What is the slack time (float) for activity A? (2 points)
5
d) What is the slack time (float) for activity D? (2 points)
0
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...Solution to Case Problem Specialty Toys
10/24/2012
I. Introduction:
The Specialty Toys Company faces a challenge of deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales. Here, I will help to analyze an appropriate order quantity for the company.
II. Data Analysis:
1.
20,0
00
.025
10,0
00
30,0
00
.025
.95
20,0
00
.025
10,0
00
30,0
00
.025
.95
Since the expected demand is 2000, thus, the mean µ is 2000. Through Excel, we get the z value given a 95% probability is 1.96. Thus, we have: z= (x-µ)/ σ=(30000-20000)/ σ=1.96, so we get the standard deviation σ=(30000-20000)/1.96=5102.
The sketch of distribution is above. 95.4% of the values of a normal random variable are within plus or minus two standard deviations of its mean.
2. At order quantity of 15,000, z= (15000-20000)/5102=-0.98,
P(stockout) = 0.3365 + 0.5 = 0.8365
At order quantity of 18,000, z= (18000-20000)/5102=-0.39,
P(stockout) = 0.1517 + 0.5= 0.6517
At order quantity of 24,000, z= (24000-20000)/5102=0.78,
P (stockout) = 0.5 - 0.2823 = 0.2177
At order quantity of 28,000, z= (28000-20000)/5102=1.57,
P (stockout) = 0.5 - 0.4418 = 0.0582
3.
Order Quantity = 15,000 |
Unit Sales | Total Cost | Sales at $24 | Sales at $5 | Profit |
10,000 |...

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