Decreasing commissions

Question

A salesperson gets a commission of $400 for the first 10,000 of sales and then $200 for each additional $10,000 or partial of sales. Let S(x) represent the commission on x dollars of sales. Find the value of S($85,000).

Answer 1

I'm not sure if they wanted you to write a function for S(t) or just figure out the problem. It's also not clear what the partial of sales means. I am assuming that if they sell 5000, then they get 1/2 the commission or $100.

 

So the first $10000, the person gets $400.

 

That leaves him the commission on $75000.

$70000 is 7 full commissions at the second rate, so that's $1400. and the last $5000 gets you $100.

 

So you would get a total of 400 + 1400 +100 = $1900 in commission.

 

In terms of function notation, this looks like this

 

S(t) = 400 + 200[ (t-10000)/10000 ] for t>=10000

 

You get the t-10000 because the second commission structure starts after the first 10000 of sales.

You get the divided by 10000 from counting the commission per 10000.

 

So (t-10000)/10000 counts how many bonuses you get.

 

So S(85000) = 400 + 200(85000-10000)

                    = 400 + 200(75000/10000) = 1900

 

Hope this helped.