please explain each step! thanks :) 5. Building a bookstore consists of six majo

Question

please explain each step! thanks :)

5. Building a bookstore consists of six major activities. According to the knowledee of activities and their inmediate predecessars, the project network is drawn Start Finish Assume that the activity time estimates (in days) for the bookstore construction project are EXPECTED ACTIVITY OPTIMISTIC | PROBABLE I PESSIMISTIC IME VARIANCE hidden hidden hidden hidden hidden hidden hidden hidden hidden hidden 0.5 0.1 0.3 hiddenhidden 10 hidden hidden hidden 0.2 . What are the expected time and variance for activity E? (ill them into the above table) b. What are the critical activities? c. What is the expected time to complete the project? d. What is the probability that the project is completed in 25 or more days?

Explanation / Answer

Expected duration of activity E

=( 2 + 4 X 3 + 7 )/6

= 3.5 days

Standard deviation of activity E = ( 7 -2 )/6 = 5/6

Hence, Variance of activity E = ( 5/6)^2 = 25/36 = 0.694

EXPECTED DURATION OF ACTIVITY E = 3.5 DAYS

VARIANCE OF ACTIVITY E = 0.694

The parallel paths and their corresponding cumulative expected durations as follows :

A-C-E-F = 4 + 6 + 3.5 + 8 = 21.5 days

A-C-F = 4 + 6 + 8 = 18 days

B-D-F = 5 + 10 + 8 = 23 days

B-C-F = 5 + 6+ 8 = 19 days

B-C-E-F = 5 +6 + 3.5 + 8 = 22.5 days

Since B-D-F has the longest expected duration, it forms the critical path

CRITICAL ACTIVITIES ARE = B, D and F

EXPECTED TIME TO COMPLETE THE PROJECT = 23 DAYS

Variance of the critical path

= Variance of B + Variance of D + Variance of F

= 0.5 + 0.3 + 0.2

= 1

Hence, Standard deviation of the critical path = Square root ( Variance ) = 1

Let Z value corresponding to the probability that the project will complete in max 25 days = Z1

Therefore ,

Expected duration of critical path + Z x Standard deviation of critical path = 25

Or, 23 + Z = 25

Or, Z = 2

Hence corresponding Probability for Z = 2 as derived from standard normal distribution table

= 0.97725

Therefore,

Probability that the project will be completed in maximum 25 days = 0.97725

Hence,

Probability that the project will be completed in 25 or more days

= 1 – Probability that the project will be completed in maximum 25 days

= 1 – 0.97725

= 0.02275

PROBABILITY THAT THE PROJECT IS COMPLETED IN MAXIMUM 25 OR MORE DAYS = 0.02275

EXPECTED DURATION OF ACTIVITY E = 3.5 DAYS

VARIANCE OF ACTIVITY E = 0.694

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