A Manufacturing Company Is Planning to Use PERT to Setup

question 11

Essay

A manufacturing company is planning to use PERT to setup a project for a new production line. For this project, they have established the following activities, precedence relationships, and time estimates in days:
$$\begin{array} { c c r r r } \text { Activity } & \text { Immediate Predecessors } & \text { Optimistic t }_p & \text { Most Likely t }_m & \text { Pessimistic t } _p\\\hline \text { a } & \text { none } & 8 & 10 & 12 \\\text { b } & \text { none } & 6 & 7 & 9 \\\text { c } & \text { b } & 3 & 3 & 3 \\\text { d } & \text { a } & 10 & 15 & 20 \\\text { E } & \text { d } & 6 & 7 & 8 \\\text { f } & \text { c } & 9 & 10 & 11 \\\text { E } & \text { d } & 5 & 7 & 10 \\\text { h } & \text { ef } & 14 & 15 & 16\end{array}$$
a. What is the expected duration for activity b?
b. What is the variance of activity d?
c. How many paths are there in the network?
d. What is the earliest finish EF) time for activity e?
e. What is the slack in days for activity c
f. What is the critical path
g. What is the duration of the critical path in days
h. What is the standard deviation of the critical path
i. What is the probability of completing the project within 50 days?

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Definitions:

Tax Rebate

A refund on taxes paid, typically when the tax liability is less than the taxes paid.

Achievement Test

A test designed to assess a person's knowledge or proficiency in a particular area or subject.

Standard Deviation

The square root of the variance, representing the distribution of a dataset in relation to its mean.

Normally Distributed

Explains a probability distribution where the distribution is balanced on either side of the mean, suggesting that data points near the mean happen more frequently than those far from the mean.