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

it's unfortunate that the 50K break points are included in the step function. Note that

[x/50k] = 0 for x<50K, but 1 for x=50K
So, assuming whole dollars, we have adjust our floor function to be

[(x-1)/50000]+1

The first plan pays
3700 for 0 <= x <= 50000
3700 + .02(x-50000) for 50000 < x

The second plan pays
(.02 + 0.01([(x-1)/50000] + 1))*x

So, when are they equal?
Looks like the 100K point marks the break:

http://www.wolframalpha.com/input/?i=plot+y%3D3700+%2B+.02(x-50000),+y%3D(.02+%2B+0.01(floor%5B(x-1)%2F50000%5D+%2B+1))*x+for+50000+%3C%3D+x+%3C%3D+200000