We want to assign seven jobs with length 2, 3, 5, 7, 11, 13, 17 on 3 identical machines. The LPT rule gives a solution with makespan 。

The LPT (Longest Processing Time) rule is a heuristic algorithm used to solve scheduling problems. In this case, we have 7 jobs with different lengths that need to be assigned to 3 identical machines.

To apply the LPT rule, we first sort the jobs in decreasing order of their processing time:

17, 13, 11, 7, 5, 3, 2

Then we assign each job to the machine with the least total processing time so far. We repeat this process until all jobs are assigned.

Using this rule, we can assign the jobs as follows:

Machine 1: 17, 7, 2 (total processing time = 26)
Machine 2: 13, 5 (total processing time = 18)
Machine 3: 11, 3 (total processing time = 14)

The makespan is the total processing time of the longest machine, which is 26. Therefore, the LPT rule gives a solution with makespan 26 for this scheduling problem.