Review the attached directed network. The number in each arc $(1,j)$ 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.

$($iv$)$ 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 any critical activity in the network.

Consider the project network given below:

The data for normal times, crash times, and crashing costs are given as follows:

$\backslash$table$[[$Job$,\backslash$table$[[$Normal Time$],[($days$)]]],[$A$,10],[$B$,5],[$C$,3],[$D$,4],[$E$,5],[$F$,6],[$G$,5],[$H$,6],[$I$,6],[$J$,4]]$