Marcus can choose between a monthly salary of $1.500 plus 5.5% of sales or $2,400 plus 3% of sales. He expects sales between $5,000 and $10,000 a month. Which salary option he choose?

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Answer 1 · 2016-11-29T12:14:32

Using the mean sales value $2400 basic + 3% commision is the better deal

As the sales figures are not fixed to a single value lets use the mean (average) value:

In statistics the notation use for this is as follows:

Dropping the $ sign for now

Let the sales value be $x$ $x$
Then the mean sales value is: $¯ x$ $barx$

$\Rightarrow ¯ x = \frac{5000 + 10000}{2} = 7500$ $=> barx=(5000+10000)/2 = 7500$

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$Option 1 - $1500 basic + 5.5% commission$ $color(blue)("Option 1 - $1500 basic + 5.5% commission")$

$1500 + \frac{5.5}{100} \times 7500 = 1912.50$ $1500+5.5/100xx7500 = 1912.50$

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$Option 2 - $2400 basic + 3% commission$ $color(blue)("Option 2 - $2400 basic + 3% commission")$

$2400 + \frac{3}{100} \times 7500 = 2625.00$ $2400+3/100xx7500 = 2625.00$

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Using the mean sales value Option 2 is the better deal