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:

$\backslash$table$[[$Activity$,\backslash$table$[[$Expected$],[$Time$]],$CRASHING COSTS $($RS$.\text{'}000)],[,\backslash$table$[[1$st$],[($in weeks$)]],\backslash$table$[[1$st$],[$Week$]],\backslash$table$[[2$nd$],[$Week$]],\backslash$table$[[3$rd$],[$Week$]]],[1-2,5,18,22,--],[2-5,8,24,25,25],[5-7,7,30,30,35],[7-11,4,15,20,--],[11-13,11,30,33,36],[1-3,4,12,24,26],[3-8,12,--,--,--],[8-11,5,40,40,40],[3-9,6,3,10,12],[9-12,9,2,7,10],[12-13,1,26,--,--],[1-4,3,10,15,25],[4-6,12,8,13,--],[6-10,9,5,12,--],[10-12,8,14,15,--]]$

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.