There are several factors that need to be taken into account when making this decision.
The urgency of the kidney transplant
Any dependents
likely clinical outcome
quality of life gained
We do not know for sure the urgency of the transplant, so just assume that they are equally urgent.
Considering the second factor, the mother with the two children may be the most obvious choice as she has two dependents whose life may be affected with the loss of their mother. Having said that, the single man who owns a big company has thousands of people dependent on him, what if he succumbs to death, what would happen to these employees. He has no family so no one can take over the business, hence the employees could lose their jobs, which may be also devastating (after all, it is not uncommon for people to commit suicide due to unemployment).
Here comes the third point, what is the likely clinical outcome for each patient? there is insufficient information. Usually we assume that the elderly man has the worst clinical outcome, and the boy may have the best(though i'm doubtful about that), but we don't know. A 60 year old man who exercises regularly, has good diet and genetically predisposed to have good general health may have a better clinical outcome than a 40 year old man who smokes, drinks, is obese and, in this case, has a stressful job.
the fourth point is, what is the quality of life gained for each patient if they receive the transplant. Arguably the young boy has a whole life ahead of him hence would have the best quality of life gained whereas the elderly man may succumb in a few years anyway, hence in this case, the boy may be the appropriate choice, but again, there is insufficient information on each patient.
it really is a tough decision to make! personally I'd go with either the young boy or the mother, but i'd be interested to hear anyone argue for the elderly man.