Problem $3$

Consider the following activity$-$on$-$arc project network, where the $12$ arcs $($arrows$)$ represent the $12$ activities $($tasks$)$ that must be performed to complete the project and the network displays the order in which the activities need to be performed. The number next to each arc $($arrow$)$ is the time required for the corresponding activity. Consider the problem of finding the longest path $($the largest total time$)$ through this network from start $($node $1)$ to finish $($node $9),$ since the longest path is the critical path. Formulate a BIP model for this problem.