$15$:$25$

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Assignment $1(2)$

Question $1$

The Airforce of Zimbabwe Aircraft Co$.$ is ready to begin a project to develop a new fighter airplane for the Zimbabwean Air Force. The company's contract with the Department of Defense calls for project completion within I$00$ weeks, with penalties imposed for late delivery. The project involves $10$ activities $($labeled $A,B,$dots,$J),$ where their precedence relationships are shown in the following project network.

Using the PERT three$-$estimate approach, the usual three estimates of the duration of each activity have been obtained as given below.

$\backslash$table$[[$Activity$,\backslash$table$[[$Optimistic$],[$Estimate$]],\backslash$table$[[$Most Likely$],[$Estimate$]],\backslash$table$[[$Pessimistic$],[$Estimate$]]],[$A$,28$ weeks,$32$ weeks,$36$ weeks$],[$B$,22$ weeks,$28$ weeks,$32$ weeks$],[$C$,26$ weeks,$36$ weeks,$46$ weeks$],[$D$,14$ weeks,$16$ weeks,$18$ weeks$],[$E$,32$ weeks,$32$ weeks,$32$ weeks$],[$F$,40$ weeks,$52$ weeks,$74$ weeks$],[$C$,12$ weeks,$16$ weeks,$24$ weeks$],[$H$,16$ weeks,$20$ weeks,$26$ weeks$],[$I$,26$ weeks,$34$ weeks,$42$ weeks$],[/,12$ weeks,$16$ weeks,$30$ weeks$]]$

$($a$)$ Find the estimate of the mean and variance of the duration of each activity.

$($b$)$ Find the mean critical path.

$($c$)$ Find the approximate probability that the project will finish within $100$ weeks.

$10$

$($c$)$ Find the approximate probability that the project will

$5$

$($d$)$ Is the approximate probability obtained in part $($c$)$ likely to be higher or lower than the true value?

$1$

CS

CamScanner

Question $2$

$\_$abel each of the following statements about the PERI three$-$estimate approach as true or false, and then justify your answer

a$)$ Activity durations are assumed to be no larger than the optimistic estimate and no smaller than the pessimistic estimate. $2$

b$)$ Activity durations are assumed to have a normal distribution.

c$)$ The mean eritical path is assumed to always require the minimom

$[2]$