Norton Industries is installing a new computer system. The activities, the activity times, and the project network are as follows.

$\backslash$table$[[$Activity$,$Time$],[$A$,3],[$B$,6],[$C$,2],[$D$,5],[$E$,4],[$F$,3],[$G$,9],[$H$,3]]$

$(1)$

complete the project in $16$ weeks. Thus, crashing of the project is necessary. The following information is relevant.

$\backslash$table$[[,$Time $($weeks$),$Cost $($$$)],[$Activity$,$Normal,Crash,Normal,Crash$],[$A$,3,1,900,1,700]]$

$\backslash$table$[[,$Time $($weeks$),$Cost $($$$)],[$Activity$,$Normal,Crash,Normal,Crash$],[$A$,3,1,900,1,700],[$B$,6,3,2,000,4,100],[$C$,2,1,500,1,000],[$D$,5,3,1,800,2,400],[$E$,4,3,1,500,1,850],[$F$,3,1,3,000,3,900],[$G$,9,4,8,000,9,800],[$H$,3,2,1,000,2,000]]$

$($a$)$ Formulate a linear programming model that can bre used to make the crashing decisions for this project. $($The objective function should be the additional cost of crashin for activity i and $y_i=$ the amount of time activity $i$ is crashed where $i=A,B,C,D,E,F,G,$ and $H.)$

Min

s$.$t$.$

constraint $A$

constraint B

$C$ depends on $A$

$D$ depends on $C$

$D$ depends on $B$

E depends on D

S depends on C

$G$ depends on $B$

H depends on $G$

$H$ depends on $F$

finish time for $H$

maximum crashing for $A$

maximum crashing for $B$

maximum crashing for $C$

maximum crashing for $D$

maximum crashing for $E$

maximum crashing for $F$

maximum crashing for $G$

maximum crashing for $H$

Solve the linear programming model and make the minimum cost crashing decisions. What is the amount of crash time $($in weeks$)$ for each activity?

$\backslash$table$[[$Activity$,$Crash Time$],[,]]$

$\backslash$table$[[$Activity$,$Crash Time$],[$A$,],[$B$,],[$C$,],[$D$,],[$E$,],[$F$,],[$G$,],[$H$,]]$

at is the added cost $($in dollars$)$ of meeting the $16-$week completion time?

velop a complete activity schedule based on the crashed activity times.

$\backslash$table$[[$Activity$,\backslash$table$[[$Earliest$],[$Start$]],\backslash$table$[[$Latest$],[$Start$]],\backslash$table$[[$Earliest$],[$Finish$]],\backslash$table$[[$Latest$],[$Finish$]],$Slack,$\backslash$table$[[$Critical$],[$Activity$]]],[$A$,,,,,,--$Select$-$