Problem $4$:

The table below gives the activity duration and precedence relationships for a small project consisting $of$ six activities. Also shown $is$ the cost per day $of$ crashing each activity and the maximum number $of$ days that each activity may $be$ crashed.

Activity

Predecessor

Normal Time $(days)$

Maximum Crashing $(days)$

$\frac{\text{\$}}{d}ay$

$1$

${?}_{?}$

$9$

$5$

$5000$

$2$

${?}_{?}$

$7$

$3$

$6000$

$3$

$1$

$5$

$3$

$4000$

$4$

$1,2$

$8$

$4$

$2000$

$5$

$3$

$6$

$3$

$3000$

$6$

$4,5$

$9$

$5$

$9000$

Determine which activities should $be$ crashed, and $by$ how much, $to$ complete the project $in22$ days.

Suppose there $isno$ specific completion time but that there $is$ a payment $of$ $$5000$ for each day that the project duration $is$ reduced below the normal completion time. Determine the optimum number $of$ days $to$ complete the project and which activities would $be$ crashed and $by$ how many days.