A salesman has to choose between two schemes of remuneration.The first scheme has a fixed salary of rs 3700 and a commission of 2% on sales above rs 50000. The second scheme has no salary but offer commission only. The commission starting from 3% of sales for the first rs 50000 or part there of increase at the rate of 1 percentage point for every increase of rs 50000 or part there of sales upto a maximum of 20% of sales. what is the minimum value of sales above which he can prefer the second scheme ?

Question

Steve · Answer

for x in sales, we have

scheme 1:
3700 + .02(x-50000)
that works out to
3700 for x <= 50000
3700 + .02x for 50000 < x <= 100000
4700 + .02x for 100000 < x <= 150000

scheme 2:
.03x for x <= 50000
1500 + .04x for 50000 < x <= 100000
3500 + .05x for 100000 < x <= 150000

I think you can figure out now how to get the place where they are equal.