A car dealership decided to add an annex to its sales office as a customer lounge. The project is divided into the activities listed in the following table. The immediate predecessor(s), times and costs, both normal and crashed, are given. To finish the project sooner, the dealership has to make time and cost tradeoffs. If the project needs to be finished in 25 weeks, you are required to formulate a linear programming model to decide about how much to crash for each activity.
Activity 
Immediate Predecessor(s) 
Time (weeks) 
Cost ($) 

Normal 
Crashed 
Normal 
Crashed 

A 
– 
5 
3 
1800 
2400 
B 
A 
7 
4 
2500 
4300 
C 
A 
6 
4 
3200 
4600 
D 
B, C 
7 
5 
2700 
3500 
E 
C 
8 
4 
3300 
3800 
F 
D 
8 
5 
2300 
2900 
G 
E 
5 
3 
4200 
4700 
H 
F, G 
6 
3 
2400 
3300 
To answer the following questions, you may want to use the last column of the following table to compute the cost of crashing an activity by one week.
Activity 
Immediate Predecessor(s) 
Time (weeks) 
Cost ($) 
Cost/Week 

Normal 
Crashed 
Normal 
Crashed 

A 
– 
5 
3 
1800 
2400 

B 
A 
7 
4 
2500 
4300 

C 
A 
6 
4 
3200 
4600 

D 
B, C 
7 
5 
2700 
3500 

E 
C 
8 
4 
3300 
3800 

F 
D 
8 
5 
2300 
2900 

G 
E 
5 
3 
4200 
4700 

H 
F, G 
6 
3 
2400 
3300 
QUESTION 45
Which of the following is a good constraint to model the fact that activity A is an immediate predecessor of activity C?
A  XaXcYc =>6  
B  Xa+Xc+Yc <=6  
C  Xa+Xc+Yc =>6  
D  Xa+Xc+Yc =>6  
E 
none of the above. 
QUESTION 46
Which of the following is a good constraint to model the fact that activity E is an immediate predecessor of activity G?
A  Yg =<5  
B  Xe+Xg+Yg =>5  
C  Xe+Xg+Yg =>3  
D  Xe+Xg+Yg =>2  
E 
none of the above. 
QUESTION 47
Which of the following represents the constraint(s) of modeling the fact that activities B and C are immediate predecessors of activity D?
A  XbXc+Xd+Yd =>7  
B  XbXc+Xd+Yd =>5  
C  Xb+Xd+Yd =>7 and Xc+Xd =>7  
D  Xb+Xd+Yd =>7 and Yg <=2  
E 
none of the above. 
QUESTION 48
Which of the following represents the constraint(s) of modeling the fact that activities F and G are immediate predecessors of activity H?
A  Xf+Xh+Yh =>6 and Xg+Xh+Yh =>6  
B  Xf+Xh+Yh =>6  
C  Xg+Xh+Yh =>6  
D  Xf+Xh+Yh =>3 and Xg+Xh+Yh =>3  
E 
none of the above. 
QUESTION 49
A constraint in the model means
A 
activity A should be finished within 2 weeks. 

B 
the total time taken by activity A cannot be more than 2 weeks. 

C 
activity A cannot be crashed by more than 2 weeks. 

D 
activity A must be finished in week 2 after the start of the activity. 

E 
none of the above. 
QUESTION 50
The right linear programming model should be?
Answer 45: Option B
Since the normal time of the predecessor “A” is less than the normal time of the activity “C” itself, therefore option B is chosen.
Answer 46: Option B
Since the normal time of the predecessor “E” is more than the normal time of the activity “G” itself, therefore option B is chosen.
Answer 47: Option A
Since the normal time of the predecessor “B & C” is less than or equal to the normal time of the activity “D” itself, therefore option A is chosen.
Answer 48: Option E
Since the normal time of activity “H” is in between the normal time of its predecessor activity “F & G” therefore no relation can be established.
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