if i sell cd's for $28 each. and i have an option to work for either straight commission of 15% or 8% and a retainer of 150 a week. how many cd's do i need to sell in a week to be better off on a straight commission
plz show working out
Your salary if you work for the 15% commission and selling x CD's is
$\displaystyle S_{15}=.15(28)x=4.2x$
$\displaystyle S_{8}=150+.08(28)x=150+2.24x$
We want to know when
$\displaystyle S_{15} \ge S_{8} \iff 4.2x \ge 150+2.24x \iff 1.96x \ge 150 \iff x \ge 76.53$
You will make more money if you sell more than 77 CD's per month.
Let x denote the number of sold CD's.
1. Your income by straight commission: $\displaystyle I_1=x \cdot 28 \cdot 15\% = x \cdot 28 \cdot \frac{15}{100}$
2. Your income by retainer and reduced commision: $\displaystyle I_2= x \cdot 28 \cdot 8\% + 150 = x \cdot 28 \cdot \frac8{100} + 150 $
3. Calculate for which value of x both incomes are equal. I've got: $\displaystyle x \geq 77$ will yield a higher income $\displaystyle I_1$
EDIT: Too fast for me, TES