$3.$ Review the attached directed network. The number in each arc $($I $,$j$)$ represents the time taken to complete the activity connecting node I and node j$.$

$($i$)$ Solve it to find the critical path in the network. Select a method of your choice to solve the problem.

$($ii$)$ Identify the critical activities. Explain how did you identify the critical path.

$($iii$)$ Estimate the floats for each critical activity. $($i$\text{'}$v$)$ Estimate the float for one non$-$critical activity.

$($v$)$ Show that increase in task time of any non$-$critical activity by one time unit does not increase the project length by one time unit.

$($vi$)$ Show it is true for anv critical activity in the network.