Consider the following data for the project newt work that corresponds to the warehouse expansion case problem.

Activity

Optimistic

Most Probable

Pessimistic

Imm. Predecessor

A

$4$

$6$

$8$

$-$

B

$6$

$8$

$16$

$-$

C

$2$

$4$

$6$

A$,$ B

D

$8$

$10$

$24$

C

E

$7$

$10$

$13$

C

F

$4$

$6$

$8$

E

G

$4$

$6$

$20$

C

H

$4$

$6$

$8$

D$,$ F$,$ G

I

$4$

$6$

$14$

D$,$ F

J

$3$

$4$

$5$

H

K

$2$

$4$

$6$

I, J

Answer the following questions taking into consideration the additional information provided.

$11$

a$.$ Develop the project newt work with activity scheduling $($i$.$e$.,$ a table defining start time and finish time of each activity as well as the slack and the critical path$).$ What is the expected project completion time? What is its corresponding variance? $[8$ Marks$]$

b$.$ Determine the probability that the project can be completed in $40$ weeks and $46$ weeks? $[4$ Marks$]$

c$.$ Using the expected activity times as the normal time and the following crashing activity information provided below. Determine the activity crashing decisions $($activities$,$ # of crashing day per activity, cost of crashing per crashed activity and the total cost$)$ in order to reduce the expected project completion time by $5$ weeks $($i$.$e$.,5$ weeks less than the expected project completion time obtained in part a$)[8$ Marks$]$

Activity

Crashed Activity Time $($Weeks$)$

Normal Cost

Crashed Cost

A

$4$

$1,000$

$1,900$

B

$7$

$1,000$

$1,800$

C

$2$

$1,500$

$2,700$

D

$8$

$2,000$

$3,200$

E

$7$

$5,000$

$8,000$

F

$4$

$3,000$

$4,100$

G

$5$

$8,000$

$10,250$

H

$4$

$5,000$

$6,400$

I

$4$

$10,000$

$12,400$

J

$3$

$4,000$

$4,400$

K

$3$

$5,000$

$5,500$