explain below a$)$

Weeks Crashed

Path

$0$

$1$

$2$

$3$

$4$

$5$

$6$

$1-2-3-4-9$

$35*$ wk$.$

$34*$

$33*$

$32*$

$31*$

$30*$

$29*$

$5-6-8-9$

$32$

$32$

$32$

$32*$

$31*$

$30*$

$29*$

$5-7-10-15$

$20$

$20$

$20$

$20$

$20$

$20$

$19$

$11-12-13-14-15$

$33$

$33$

$33*$

$32*$

$31*$

$30*$

$29*$

Activity Crashed

$4$

$1$

$4,13$

$9,12$

$9,11$

$1,5,13$

Crash Cost

$$15$

$$18$

$$20+5$

$$30+8$

$$33+10$

$$22+12+12$

Cumul. Crash Cost

$$15$

$$33$

$$58$

$$96$

$$139$

$$185$

$*=$ Critical path

b$)$ The optimum number of weeks to crash the project is four weeks, because after that time the cost to crash one more week $($$$43,000)$ would be greater than the indirect cost savings for a week $($$$40,000).$