Question

A life-insurance salesman spends 9 hours a week on the telephone soliciting new clients. From past experience, the salesman estimates that each hour spent calling students, blue-collar workers, and professionals will produce the following number of additional sales:

	Number of Additional Sales
Hours Calling	Students	Blue-Collar Workers	Professionals
1	10	8	14
2	8	6	11
3	6	4	8
4	4	3	6
5	1	1	4
6	0	0	1

a.   How should the life-insurance salesman allocate his phone-calling time to maximize the number of sales?

Hours spent calling students = ______

Hours spent calling blue-collar workers = ______

Hours spent calling professionals = ______

b.   Now suppose the salesman decides to spend 16 hours a week soliciting new clients. How should he allocate his time?

Hours spent calling students = ______

Hours spent calling blue-collar workers = ______

Hours spent calling professionals = ______

Answer 1

a) The total number of hours given is 9.

The insurance salesman would gain 14 new clients if he spends the first hour in calling professionals which is higher than the two of them.Similarly if the second hour is also spend on professionals, the gain is more than anywhere else. In the third hour, 10 clients would be gained if time is spent on students , which is higher than spending a third hour on professionals or first hour on blue collar workers.

After that two hours each would be spend on all three categories.

i) Hours spent calling students: 3 hours (ie till 6)

ii) Hours spent calling blue collar workers= 2 hours ie till 6

iii) Hours calling professionls= 4 hours ie till 6.

All three are equal and total hours are 9. So the salesman would maximise his sales in these 9 hours.

b) If the salesman spends 16 hours rather than 9, then instead of starting from top, we would begin from bottom. The total number of hours spend when all three are equally called is 6*3= 18 hours. Out of these now 16 hours are to be maximised. So the salesman can elinimate the two hours , each of student and blue collar worker, where his sales is zero ie in the sixth hour.

i) Hours spend calling students = 5 hours till sale is one.

hours spend on blue collar= 5 hours till sale is 1

hours spend on professionals= 6 hours till sale is 1.

so the number of hours spend is 5+5+6=16 hours and the sales is also maximised.

(you can comment for doubts)