1. The standard deviation of the critical path is

1. 1. 0.33

   
   
   

   2. 0.55

   
   
   

   3. 0.88

   
   
   

   4. 1.66

   
   
   

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1. View Hint View Answer Discuss in Forum

   Variance =		tp − tO		2
   		6

   
   
   

   Total variance =		1		2	+		2		2	+		1		2	+		1		2
   		3					3					3					3

   
   

   =	7
   	9

   
   Standard deviation = √variance
   ⇒  √7/9 = 0.88

   Correct Option: C

   Variance =		tp − tO		2
   		6

   
   
   

   Total variance =		1		2	+		2		2	+		1		2	+		1		2
   		3					3					3					3

   
   

   =	7
   	9

   
   Standard deviation = √variance
   ⇒  √7/9 = 0.88

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2. If an additional constraint X₁ + X₂ ≤ 5 is added, the optimal solution is

1. 1. (5/3, 5/3)

   
   
   

   2. (4/3,4/3)

   
   
   

   3. (5/2, 5/2)

   
   
   

   4. (5, 0)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Max z = x₁ + x₂
   
   As feasibly region remains the same solution remains the same (4/3, 4/3).
   Hence, the correct option is (b).

   Correct Option: B

   Max z = x₁ + x₂
   
   As feasibly region remains the same solution remains the same (4/3, 4/3).
   Hence, the correct option is (b).

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3. Let Y₁ and Y₂ be the decision variables of the dual and v₁ and v₂ be the slack variables of the dual of the given linear programming problem. The optimum dual variables are

1. 1. Y₁ and Y₂

   
   
   

   2. Y₁ and v₁

   
   
   

   3. Y₁ and Y₂

   
   
   

   4. v₁ and v₂

   
   
   

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1. View Hint View Answer Discuss in Forum

   The optimal dual variables are V₁ & V₂.

   Correct Option: D

   The optimal dual variables are V₁ & V₂.

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4. The critical path duration of the network (in days) is

1. 1. 11

   
   
   

   2. 14

   
   
   

   3. 17

   
   
   

   4. 18

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   EST = Earliest start time
   LFT = Latest Finish Time
   ∴  Path along which EST & LFT is equal are called critical path
   Critical path duration is 18 days.

   Correct Option: D

   
   EST = Earliest start time
   LFT = Latest Finish Time
   ∴  Path along which EST & LFT is equal are called critical path
   Critical path duration is 18 days.

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5. A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:
   
   If all activities other than S take the estimated amount of t i me, t he maxi mum dur at i on (in weeks) of the activity S without delaying the completion of the project is ______.

1. 1. 2

   
   
   

   2. 9

   
   
   

   3. 13

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: A

   

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