Problem $1(15$ points$)$

Consider the project with the listed $[$AOA$]$ activities. Normal durations and costs, as well as crash

durations and costs are listed for each activity. Precedence relationships are implicitly given by the

activity names $($e$.$g$.,$ activity $(1,2)$ is represented as an arc from node $1$ to node $2).$

$*$Times are in weeks.

$**$Assume partial crashing is acceptable for ALL activities.

$($a$)$ Assuming that all activities are completed according to their normal durations, how long will it take

to complete the project?

$($b$)$ Suppose that you wanted to shorten the duration of the project by $3$ weeks. Which activities would

you shorten, and by how much? What additional cost would you incur by doing this?