You are the project manager working for Mack's Pool Co$.$ Your project consists of installing a new hot tub at a client's patio. You would like to find the minimum cost schedule for your project. There is a $$50$ per week penalty for each week the project is delayed beyond week $13.$ In addition, your project team determined that indirect costs are $$15$ per week.

ACTIVITY

Immediate Predecessor $($s$)$

NORMAL TIME $($NT$)$

CRASH TIME $($CT$)$

Normal Cost $($NC$)$

Crash Cost $($CC$)$

A

$--$

$2$

$1$

$50$

$70$

B

A

$4$

$2$

$80$

$160$

C

A

$8$

$4$

$70$

$110$

D

A

$6$

$5$

$60$

$80$

E

B

$7$

$6$

$100$

$130$

F

D

$4$

$3$

$40$

$100$

G

C$,$ E$,$ F

$5$

$4$

$100$

$150$

Before crashing, the project duration is $\_\_\_\_\_\_\_\_\_$ week$($s$).$