Question

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 ?

I Have seen the solutions which posted by your faculty's please help me out by doing step by step please easy & simplified way

Answer 1

The payment for scheme 1 is:
3700 for 0 <= x <= 50000
3700+.02(x-50000) for x > 50000
so, for various amounts above that, we have
50000: 3700 + 1000 = 4700
100000: 3700 + 1500 = 5200
150000: 3700 + 2000 = 5700

For scheme 2, we have breakpoints at:
50000: .03*50000 = 1500
100000: 1500 + .04*50000 = 3500
150000: 3500 + .05*50000 = 6000

So, you can see that somewhere near 150,000 the 2nd plan starts paying more than the 1st plan.

You should be able to figure out where:

3700 + .02(x-50000) = 3500 + .05(x-100000)