A Construction Project has indirect costs totalling Rs$.40,000$ per week. The major activities in the project and their expected times are shown in the TABLE below: $(12)$

Activity Expected Time CRASHING COSTS $($RS$.\text{'}000)$

$($in weeks$)1$st Week $2$nd Week $3$rd Week

$1-251822--$

$2-58242525$

$5-77303035$

$7-1141520--$

$11-1311303336$

$1-34122426$

$3-812------$

$8-115404040$

$3-9631012$

$9-1292710$

$12-13126----$

$1-43101525$

$4-612813--$

$6-109512--$

$10-1281415--$

a$.$ Determine the optimum time$-$cost crashing plan.

b$.$Tabulate the total cost values and find the least expensive crashing schedule that would reduce the project duration by six weeks.