$\backslash$table$[[$ID$,$Activity,Predecessor,Duration$],[$A$,$Prepare Site,None,$2],[$B$,$Pour Foundation,A$,3],[$C$,$Erect Frame,B$,4],[$D$,$Roof,C$,4],[$E$,$Windows,C$,1],[$F$,$Doors,C$,1],[$G$,$Electrical,C$,3],[$H$,$Rough$-$In Frame,D$,$E$,$F$,2],[$I$,$Door Opener,F$,$ G$,1],[$J$,$Paint,H$,$ I,$1],[$K$,$Clean Up$,2,]]$This assignment is meant for you to practice the critical path method. Use the PDM network diagramming method to determine the critical time for the project below.

You have signed a contract to build a garage for the Simpsons. You will receive a $$500$ bonus for completing the project within $21$ days. The contract also contains a penalty clause in which you will lose $$100$ for each day the project takes longer than the agreed $21$ days.

Draw a project network given the information below. Then, do the following:

$1.$ Complete the forward and backward pass

$2.$ Determine the critical path

$3.$ Compute the Total slack for all activities

$4.$ Determine which activities have free float

Then answer the following questions.$\backslash$table$[[$ID$,$Activity,Predecessor,Duration$],[$A$,$Prepare Site,None,$2],[$B$,$Pour Foundation,A$,3],[$C$,$Erect Frame,B$,4],[$D$,$Roof,C$,4],[$E$,$Windows,C$,1],[$F$,$Doors,C$,1],[$G$,$Electrical,C$,3],[$H$,$Rough$-$In Frame,D$,$E$,$F$,2],[$I$,$Door Opener,F$,$ G$,1],[$J$,$Paint,H$,$ I,$1],[$K$,$Clean Up$,2,]]$

Question $1$

Upload the working calculations that show the critical path, including the forward and backward passes.

Question $2$: What is the critical time for this project?

A $20$ days

B $18$ days

C $19$ days

D $21$ days

Question $3$

There will be a two$-$day penalty based on the critical time calculated. This statement is:

True

False

Question $4$

What is the total float of the activity "Windows"?

A $3$ days

B $2$ days

C $1$ day

D Zero float

Question $5$

What is the free float of the activity "doors", with the successor activity "door opener"?

$1$ day

zero days

$3$ days

$2$ days

Question $6$

After some negotiation with the Simpsons, they have agreed to a new end date. What would the project float be if you had to complete the project in $25$ days?

zero days

$5$ days

$7$ days

$8$ days

Question $7$

What is the total float of Activity C $-$ "Erect Frame"?

Zero days

$2$ days

$3$ days

Question $8$

Will you receive a bonus or a penalty at the end based on your original critical time?

Bonus

Penalty

Question $9$

What is the early start $($ES$)$ of activity J $-$ "Paint"?

Day $15$

Day $17$

Day $19$

Day $16$

Question $10$

A new resource has been assigned to task G "Electrical". This resource takes one day extra to complete the task. The new duration of the task is $4$ days. The critical time:

Remains the same

Has increased by $1$ day

Has increased by $2$ days

The critical time is now $19$ days

Question $11$

Use the original information posted for this question.

The task I $-$ "Door Opener" has a specialist working on it$.$ However, a new resource has been assigned and he takes $5$ days to complete the task. Based on this change, there are two opinions: the Simpsons and the Project Team. The Simpsons think it will now complete in $22$ days, however, the project team thinks it will take $21$ days. Who is correct?

The project team

The simpsons

They are both wrong