A project has the activity duration and cost information indicated in the table where all times are in weeks. What is the lowest total cost for completing this project in $33$ weeks?

Activity

Normal time

Crash time

Normal Cost

Crash Cost

Predecessor

A

$8$

$5$

$$1,000$

$2,000$

$$

B

$6$

$4$

$1,500$

$2,000$

A

C

$8$

$5$

$1,800$

$2,300$

A

D

$12$

$9$

$1,000$

$1,800$

B

E

$14$

$11$

$950$

$1,450$

B

F

$9$

$7$

$1,500$

$1,900$

C$,$ D

G

$7$

$5$

$2,300$

$2,800$

E$,$ F

$$11,250$

$$11,500$

$$12,250$

$$12,500$