Question

You and your friends hike a total of 8 miles to the nearest campsite (Activity A). Upon arriving you break off into teams. One team will set up tents and hammocks for everyone to sleep in (Activity B). At the same time, another team will get wood for a fire (Activity C). Once they have the wood, that same team then proceeds to start the fire (Activity D). The third team will walk to find water (Activity E) and once they find it they will to collect water and bring it back to camp (Activity F). Once the fire is ready and the water is brought back to camp the two groups- the one collecting firewood and the one collecting water- will then purify the water (Activity G). Once the camp is set up and the water is purified everyone will come together and cook dinner around the campfire (Activity H). Once dinner is prepared and eaten half of the group stays behind to put out the fire (Activity I) and half of the group walks away from the campsite to dispose of the food waste (Activity J). After disposing of the food waste the second half of the group returns to the camp (Activity K). Once everyone is at the campsite the day of camping ends

Activity Optimistic time Most Likely Time Pessimistic Time
to complete to Complete to Complete
A Hike to the campsite 3 5 8
B Set up campsite 2 4 5
C Collect wood for fire 1 3 5
D Start a fire 1 2 3
E Find water 0.5 1 3
F Collect water and bring it 1 2 4
back to canm
G Purify the water 1 2 4
H Cook and eat dinner 1 3 4
I Put out fire 1 2 4
J Dispose of food waste 0.5 2 3
K Return from food waste disposal 0.25 1 2
a. Determine the critical path of the PERT chart in a.
b. Assuming a deterministic system how long will it take to complete the entire process.

Answer 1

a. The critical path is 16 minutes.

b. The length of time to complete the entire process = 23 minutes.

Step-by-step explanation:

a) Data and Calculations:

Activity Optimistic time Most Likely Time Pessimistic Time

to complete to Complete to Complete

A Hike to the campsite 3 5 8

B Set up campsite 2 4 5

C Collect wood for fire 1 3 5

D Start a fire 1 2 3

E Find water 0.5 1 3

F Collect water & bring it

back to camp 1 2 4

G Purify the water 1 2 4

H Cook and eat dinner 1 3 4

I Put out fire 1 2 4

J Dispose of food waste 0.5 2 3

K Return from food

waste disposal 0.25 1 2

Total time 12.25 27 45

Critical path: Activity A - Activity B

Activity A - Activity C 3 - Activity D 2 - Activity E 1 - Activity F 2

Activity G 2 - Activity H 3 - Activity I and J 2 - Activity K 1

= 3 + 2 + 1 + 2+ 2 + 3 + 2 + 1 = 16 minutes

Length of time to complete the entire process = 27 - 4 = 23

The critical path identifies the longest stretch of dependent activities and measuring the time required to complete them from start to finish.