Question

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

1. Which of the following is a good constraint to model the fact that activity A is an immediate predecessor of activity C?

   A		Xa-Xc-Yc =>6
   B		-Xa+Xc+Yc <=6
   C		-Xa+Xc+Yc =>6
   D		Xa+Xc+Yc =>6
   E		none of the above.

QUESTION 46

1. 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

1. Which of the following represents the constraint(s) of modeling the fact that activities B and C are immediate predecessors of activity D?

   A		-Xb-Xc+Xd+Yd =>7
   B		-Xb-Xc+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

1. 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

1. 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

1. The right linear programming model should be?

Answer 1

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.