Question

You wish to build a house and you have divided the process into a number of tasks, namely:

Answer 1

Answer:

x1 + x2 + x3 + x4 + x5 + x6 + x7

Explanation:

Formulating the problem as an LP

Attached below is an AOA diagram and the completion time of each task is indicated in the diagram, The diagram was based on the conditions given for the completion of each task accordingly.

To complete the project as early as possible we will have assume

x1, x2, x3, x4, x5, x6, and x7 to be the times taken to complete each node

hence the earliest time taken to complete the project

= x1 + x2 + x3 + x4 + x5 + x6 + x7

when : x2 - x1 ≥ 3

           x3 - x2 ≥ 2

           x4 - x2 ≥ 2

           x5 - x3 ≥ 3

           x6 - x3 ≥ 3

           x7 - x5 ≥ 1

           x7 - x6 ≥ 1

also : x1, ............ , x7 ≥ 0