A machine operator has to perform three operations, namely plane turning, step turning, & taper turning on a number of different jobs. The time required to perform these operations in minute for each operating for each job given in the matrix given below find the optimal sequence, which minimizes the time required.

Job

Time for plane Turning (in min)

Time for step Turning (in min)

Time for taper turning (in min)

1

3

8

13

2

12

6

14

3

5

4

9

4

2

6

12

5

9

3

8

6

11

1

13

1
4-3-5-6-2-1
2
4-3-6-1-2-5
3
4-3-1-6-2-5
4
4-3-5-2-6-1

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