1. ## Function construction.

Hey folks, I have the following question, and I was hoping one of you pros could check my answer against yours or let me know if there is a better answer, mine is pretty convoluted and bulky.

The question is;

A salesman has a base salary of $28,000.00, and earns in addition a 5% commission per unit for the first 100 units sold, 7.5% for the next 100 units sold, and 12% for any additional units sold (i.e. above 200). a. If the market price per unit is$75.00, give the function of the income earned in terms of units sold.
Now I put together the following, and it feels way to bulky, not sure if I'm making this more complicated than it is.

$\displaystyle f(u)=28000+(0.05)(75)u+(0.025)(75)(u-100)+(0.045)(75)(u-200)$

What do you guys think? Thanks!
Kasper

2. hi
i agree with what you wrote,your function is correct for any $\displaystyle u\geq 100$,but you still need confirmation

3. Originally Posted by Kasper
Hey folks, I have the following question, and I was hoping one of you pros could check my answer against yours or let me know if there is a better answer, mine is pretty convoluted and bulky.

The question is;

Now I put together the following, and it feels way to bulky, not sure if I'm making this more complicated than it is.

$\displaystyle f(u)=28000+(0.05)(75)u+(0.025)(75)(u-100)+(0.045)(75)(u-200)$

What do you guys think? Thanks!
Kasper
$\displaystyle f\left( u \right) = \left\{ \begin{gathered} 28000 + 0.05(75)u,{\text{ if }}0 < u \leqslant 100 \hfill \\ 28000 + 0.05(75)100 + 0.075(75)(u - 100),{\text{ if }}100 < u \leqslant 200 \hfill \\ 28000 + 0.05(75)100 + 0.075(75)100 + 0.12(75)(u - 200),{\text{ if }}u > 200 \hfill \\ \end{gathered} \right.$

$\displaystyle \Rightarrow f\left( u \right) = \left\{ \begin{gathered} 28000 + 3.75u,{\text{ if }}0 < u \leqslant 100 \hfill \\ 28375 + 5.625(u - 100),{\text{ if }}100 < u \leqslant 200 \hfill \\ 28937.50 + 9(u - 200),{\text{ if }}u > 200 \hfill \\ \end{gathered} \right.$

does that seems good?

4. Originally Posted by Shyam
$\displaystyle f\left( u \right) = \left\{ \begin{gathered} 28000 + 0.05(75)u,{\text{ if }}0 < u \leqslant 100 \hfill \\ 28000 + 0.05(75)100 + 0.075(75)(u - 100),{\text{ if }}100 < u \leqslant 200 \hfill \\ 28000 + 0.05(75)100 + 0.075(75)100 + 0.12(75)(u - 200),{\text{ if }}u > 200 \hfill \\ \end{gathered} \right.$

$\displaystyle \Rightarrow f\left( u \right) = \left\{ \begin{gathered} 28000 + 3.75u,{\text{ if }}0 < u \leqslant 100 \hfill \\ 28375 + 5.625(u - 100),{\text{ if }}100 < u \leqslant 200 \hfill \\ 28937.50 + 9(u - 200),{\text{ if }}u > 200 \hfill \\ \end{gathered} \right.$
i thought 28000 will remain the same,i don't get it