A project has four possible paths, as shown below with their associated path lengths.

Paths Length

ACF $9$ weeks

ACDF $12$ weeks

BDF $10$ weeks

BEF $10$ weeks

Every activity except activity A can be crashed for a cost given in the second table below.

Activity Crashable weeks $$/$week cost to crash

A $0-$

B $2$ $$90$

C $1$ $$100$

D $3$ $$130$

E $1$ $$80$

F $1$ $$200$

Determine the shortest length of time to complete the project after crashing by filling in the table below. The last $4$ rows keep track of the length of each of the paths. For each Step $($column$)$: $($i$)$ in the $2$nd row, enter the activity that is crashed in that step and the corresponding cost, and then $($ii$)$ enter the new path length for each path in the $4$ cells below. $($For example, if you crashed both B and C in Step $1($which is not correct$),$ you would enter $"$B$+$C$,$ $$190"$ in row $2$ for Step $1.)$ Note that the correct answer may not use all $7$ Steps!

$2.$ Determine the total cost for crashing the project: $\_\_\_\_\_\_\_\_\_\_$

$($Remember$,$ you should crash only $1$ week at a time, so each column in the table below reduces the length of the project by exactly one week. See Topic $7$b$.)$

Step $1$ Step $2$ Step $3$ Step $4$ Step $5$ Step $6$ Step $7$

Path Initial length

ACF $9$

ACDF $12$

BDF $10$

BEF $10$