Question $3(25$ POINTS$)$:

Consider the list of activities and predecessors that are summarized in following table.

a$.$ Draw the AOA project diagram.

b$.$ Determine the length of the critical path and the

critical activities for this project.

c$.$ Determine free floats of activities $D$ and $J.$

d$.$ This project must be completed in $38$ weeks. The

time required to complete each activity can be

reduced by up to $3$ weeks with given costs.

Formulate the linear programming model in order

to minimize the cost of meeting the project

deadline.