Problem $2.($Project Crashing.$)$ Consider the project network described in the following table, in

which $Tn$ and $Tc$ are in days and $Cn$ and $Cc$ are in $$1,000$ s$.$

Please follow the class example to formulate a Linear Program that crashes the project by at

least $3$ days with minimum crashing cost. Let's assume that the project starts on day $1$ and

define the decision variables to be:

$x_i$ : earliest start $($ES$)$ time of activity $i$

$Y_i$ : # days to be shorten for activity $i$

$($You do not need to Solve the model with Solver.$)$