Q$\mathrm{.}6$Set. $($A$)$ For a given project, duration and resource requirements are given below $[3+2+2]$

Activity Duration $($weeks$)$ Machines Crew size $($Men$)$

$1-27220$

$1-37220$

$2-38330$

$2-46430$

$3-69220$

$4-53220$

$5-65220$

Resources AVAILABILITY: $($A$)$ Machines $4($B$)$ Men $40$

a$)$ Draw the network diagrm, identify the critical path assuming that there are no resource constraints.

b$)$ Draw the time scale network as per EST and level the resources

c$)$ Find the project completion time under the given resource constraint.