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Problem $9-19($Algorithmic$)$

The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group. The group's leader turned to PERT$/$CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. The project network is as follows:

The activity time estimates $($in weeks$)$ are as follows:

Activity Optimistic Most Probable Pessimistic

A $2\mathrm{.}03\mathrm{.}04\mathrm{.}0$

B $2\mathrm{.}03\mathrm{.}58\mathrm{.}0$

C $4\mathrm{.}09\mathrm{.}014\mathrm{.}0$

D $4\mathrm{.}06\mathrm{.}014\mathrm{.}0$

E $3\mathrm{.}04\mathrm{.}05\mathrm{.}0$

F $1\mathrm{.}03\mathrm{.}05\mathrm{.}0$

G $7\mathrm{.}08\mathrm{.}513\mathrm{.}0$

H $5\mathrm{.}56\mathrm{.}06\mathrm{.}5$

I $2\mathrm{.}06\mathrm{.}010\mathrm{.}0$

J $2\mathrm{.}02\mathrm{.}56\mathrm{.}0$

Develop an activity schedule for this project and identify the critical path activities.

If required, round your answers to two decimal places. If your answer is zero enter $0.$

Activity Expected Time Variance

A fill in the blank $1$

$3\mathrm{.}00$

fill in the blank $2$

$0\mathrm{.}11$

B fill in the blank $3$

$4\mathrm{.}58$

fill in the blank $4$

$2\mathrm{.}89$

C fill in the blank $5$

$9\mathrm{.}50$

fill in the blank $6$

$5\mathrm{.}25$

D fill in the blank $7$

$8\mathrm{.}00$

fill in the blank $8$

$5\mathrm{.}44$

E fill in the blank $9$

$4\mathrm{.}00$

fill in the blank $10$

$0\mathrm{.}33$

F fill in the blank $11$

$2\mathrm{.}33$

fill in the blank $12$

$0\mathrm{.}11$

G fill in the blank $13$

$8\mathrm{.}58$

fill in the blank $14$

$2\mathrm{.}58$

H fill in the blank $15$

$6\mathrm{.}17$

fill in the blank $16$

$0\mathrm{.}08$

I fill in the blank $17$

$6\mathrm{.}00$

fill in the blank $18$

$2\mathrm{.}33$

J fill in the blank $19$

$3\mathrm{.}25$

fill in the blank $20$

$0\mathrm{.}42$

Earliest Latest Earliest Latest Critical

Activity Start Start Finish Finish Slack Activity

A fill in the blank $21$

$0$

fill in the blank $22$

$3$

fill in the blank $23$

$0$

fill in the blank $24$

$3$

fill in the blank $25$

$0$

Yes

B fill in the blank $27$

$3\mathrm{.}00$

fill in the blank $28$

$7\mathrm{.}58$

fill in the blank $29$

$3\mathrm{.}00$

fill in the blank $30$

$7\mathrm{.}58$

fill in the blank $31$

$0$

Yes

C fill in the blank $33$

$7\mathrm{.}58$

fill in the blank $34$

$17\mathrm{.}08$

fill in the blank $35$

$7\mathrm{.}58$

fill in the blank $36$

$17\mathrm{.}08$

fill in the blank $37$

$0$

Yes

D fill in the blank $39$

$7\mathrm{.}58$

fill in the blank $40$

$15\mathrm{.}58$

fill in the blank $41$

$7\mathrm{.}58$

fill in the blank $42$

$15\mathrm{.}58$

fill in the blank $43$

$7\mathrm{.}58$

Yes

E fill in the blank $45$

$3\mathrm{.}00$

fill in the blank $46$

$7\mathrm{.}00$

fill in the blank $47$

$7\mathrm{.}58$

fill in the blank $48$

$11\mathrm{.}58$

fill in the blank $49$

$4\mathrm{.}58$

No

F fill in the blank $51$

$0$

fill in the blank $52$

$2\mathrm{.}33$

fill in the blank $53$

$11\mathrm{.}58$

fill in the blank $54$

$13\mathrm{.}91$

fill in the blank $55$

$0$

Yes

G fill in the blank $57$

$17\mathrm{.}08$

fill in the blank $58$

$25\mathrm{.}66$

fill in the blank $59$

$17\mathrm{.}08$

fill in the blank $60$

$25\mathrm{.}66$

fill in the blank $61$

$0$

Yes

H fill in the blank $63$

$15\mathrm{.}58$

fill in the blank $64$

$21\mathrm{.}75$

fill in the blank $65$

$15\mathrm{.}58$

fill in the blank $66$

$21\mathrm{.}75$

fill in the blank $67$

$0$

Yes

I fill in the blank $69$

$21\mathrm{.}75$

fill in the blank $70$

$27\mathrm{.}75$

fill in the blank $71$

$21\mathrm{.}75$

fill in the blank $72$

$27\mathrm{.}75$

fill in the blank $73$

$0$

Yes

J fill in the blank $75$

$13\mathrm{.}91$

fill in the blank $76$

$17\mathrm{.}16$

fill in the blank $77$

$25\mathrm{.}57$

fill in the blank $78$

$31\mathrm{.}00$

fill in the blank $79$

$13\mathrm{.}00$

No

Critical Path:

B$-$F$-$J

What is the probability that the project will be completed so that Landon Corporation may introduce the new product within $25$ weeks? Within $30$ weeks?

Expected project completion time $=$ fill in the blank $82$

$27\mathrm{.}75$

weeks. If required, round your answer to two decimal places.

fill in the blank $83$

$3\mathrm{.}32$

$.$ If required, round your answer to two decimal places.

P$(25$ weeks$)=$ fill in the blank $84$

$0\mathrm{.}0869$

$.$ If required, round your answer to four decimal places.

P$(30$ weeks$)=$ fill in the blank $85$

$0\mathrm{.}9772$

$.$ If required, round your answer to four decimal places.