Q$\mathrm{.}3.$ The following table shows for each activity needed to complete the project, the normal time, the shortest time in which the activity can be completed of a building contract and the increase in cost per day for reducing the time of each activity. The contract includes the penalty clause of Rs $1000$ per day over $17$ days. The overhead $($Indirect$)$ Cost per day is Rs $1600.$ The cost of completing the eight activities in normal time is Rs$.65000.$ Calculate the lowest cost and the associated project duration. Justify your answer.

$\backslash$table$[[$Activity$,\backslash$table$[[$Normal$],[$duration$]],$Crash duration,Cost increase$/$ day $($Rs$.)],[1-2,6,4,500],[1-3,8,4,\backslash$table$[[400$ for first two days each and $900$ for$],[$next two days each$]]],[1-4,5,3,300],[2-4,3,3,-],[2-5,5,3,800],[3-6,12,8,\backslash$table$[[800$ for first three days each and $2000],[$for next one day$]]],[4-6,8,5,500],[5-6,6,6,-]]$

$(25)$