Assume that the first schedule finishes job 1 at time f1 and finishes job 2 at time f2. Assume that the second schedule finishes job 2 at time f'2 and then finishes job 1 at time f'1. We want to know if w1f1+w2f2 is greater than w2f'2+w1f'1
We then conclude that f2=f'1. We also conclude that f1 = f'1 - f'2 since both are equal to t1, the duration of job 1.
Putting it all together, we use the two queations to eliminate two out of the four quantitites, f1, f2, f'1, and f'2. We then write down our test in terms of only two of the "f" variables, and w1 and w2.
Now, we know the test or algorithm for two jobs. We need to derive an algorithm for n jobs.