## Industrial Engineering Miscellaneous

#### Industrial Engineering

1. The standard deviation of the critical path is

1.  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

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

1. 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).

1. 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. The optimal dual variables are V1 & V2.

##### Correct Option: D

The optimal dual variables are V1 & V2.

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

1. 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.

1. 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 ______.