Problem 6 The sequence of main activities in the construction of two structures
ID: 3328317 • Letter: P
Question
Problem 6 The sequence of main activities in the construction of two structures is shown in the figure below. The construction of the superstructures A and B can start as soon as their common foundation has been completed. The possible times of completion for each phase of construction are indicated in the figure; for example, the foundation phase may take 5 or 7 months. A) Foundation (5,7) Start o Finish (a) List the possible combinations of construction times for each phase of the project; for example, (5,3,6) denotes the event that it takes 5 months for foundation, 3 months for superstructure A, and 6 months for superstructure B (b) What are the possible total completion times for structure A alone? For structure B alone? (c) What are the possible total completion times for the project? d) If the sample points in part (a) are equally likely, what is the probability that the complete project will be finished within 10 months?Explanation / Answer
a)
total sample space are the ways we can arrange (5,7) (3,4) (4,6)
{(5,3,4)(5,3,6)(5,4,4)(5,4,6)(7,3,4)(7,3,6)(7,4,4)(7,4,6)}
b)
For A alone
{(5,3)(5,4)(7,3)(7,4)} is 8,9,10,11 months
For B alone
{(5,4)(5,6)(7,4)(7,6)} is 9,11,13 months
c)
{(5,3,4)(5,3,6)(5,4,4)(5,4,6)(7,3,4)(7,3,6)(7,4,4)(7,4,6)}
Total comp time is 9 or 11 or 13 months
d)
P(project completes within 10 months is 2/8 =0.25