Exercise $2[50$ pts$]$

The following vacuum cleaner company is performing the feasibility study of launching a new

product. The following information is gathered. This includes the product testing, manufacturing.

cost estimation, marketing research,... $.$ The activities that make up the project are identified with

their duration, their immediate predecessor, as well as the optimistic, most probable and

pessimistic duration for each activity are summarised in the following Table $2.$

Table $2$: Information about the activities

Part $1$: Here consider firat deterministic durations

$($i$)$ Construct the corresponding network

$($ii$)$ Using CPM$,$ determine the critical path and the total duration of the project.

$10$

$($iii$)$ Show the corresponding Gantt Chart and discuss bow long some of the activitiea could be

delayed without affecting your decision $($es; completing the project on time, consider

activity G say$)$

Part $2$: Now consider the uncertain duration:

Given the uncertain duration of the activities and the estimates given in Table $1,$ use DERT to

a$)$ find the expected time and the variance for each activity. $[10]$

b$)$ determine the corresponding critical path, the expected total duration of the project

and its corresponding variance.

c$)$ calculate the probability of completing the project within $20$ weeks.

please solve part $1$ and $2$