Question

Sales people at Spinner Electronics are paid on commission. They receive a percentage of their sales for a given month. If their sales is less than or equal to $2,500 they receive 25% of sales. For sales greater than $2,500 and less than or equal to $4,500 the rate is 22% of sales, and if their sales amount is greater than $4,500 they receive 20% of sales. Using x to represent the amount of sales, write a piecewise function, c(x) to represent this commission structure.

Answer 1

Explanation:

The piecewise function

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c(x) representing the commission structure for sales at Spinner Electronics can be defined as follows:

0.25x & \text{if } 0 \leq x \leq 2500 \\

0.22x & \text{if } 2500 < x \leq 4500 \\

0.20x & \text{if } x > 4500

\end{cases}\]

In this piecewise function:

- For sales (\(x\)) less than or equal to $2,500, the commission rate is 25% of sales (\(0.25x\)).

- For sales (\(x\)) greater than $2,500 and less than or equal to $4,500, the commission rate is 22% of sales (\(0.22x\)).

- For sales (\(x\)) greater than $4,500, the commission rate is 20% of sales (\(0.20x\)).

So, depending on the value of \(x\) (the amount of sales), the function \(c(x)\) calculates the commission accordingly.