$7-1.$ Consider the following problem:

For computations, use Excel. For drawing, you can utilize Excel or Word. Refer to the Solved Problem example for some hints. Feel free to utilize Excel QM or QM for Windows to verify your answers.

Tom Marcus, a director of personnel at Management Resources, Inc., is in the process of designing a program that its customers can use in the job$-$finding process. Some of the activities include preparing resumes, writing letters, making appointments to see prospective employers, researching companies, and industries, and so on$.$ Necessary information on the activities is shown in the following table:

DAYS

ACTIVITY o $($otimistic$)$ p $($pessimistic$)$ m $($most likely$)$

IMMEDIATE PREDECESSORS

A $465-$

B $285-$

C $597$ A

D $465$ A

E $264$ B

F $396$ B

G $101211$ C$,$ E

H $798$ D$,$ F

Required:

$($a$).$ Construct a network for this problem.

$($b$).$ Compute the expected time for each activity, also the variance. Note: Expected time $=($optimistic time $+$ pessimistic time $+4*$ most likely$)/6.$ Variance $=($pessimistic $-$ optimistic$)^2/36.$

$($c$).$ Determine ES$,$ EF$,$ LS$,$ LF$,$ and slack for each activity.

$($d$).$ Determine the critical path and project completion time. Also the standard deviation for the completion time. Note: To compute the standard deviation of the project completion time, you need to sum the variances of the the critical path activities, and then take the square root of that sum.

$($e$).$ Determine the probability that the project will be finished in $23$ days or less.

$($f$).$ Determine the probability the the project will NOT be finished in $26$ days or less.

$($g$).$ Determine the probability that the project will be finished in $25$ days or less.

$($h$).$ If a manager considers crashing any of the tasks to reduce the duration of the project completion time, which tasks should he$/$she focus on$?$ Why?