An air conditioning salesperson receives a base salary of $2850 per month plus a commission. The commission is 2% of the sales up to and including $25,000 for the month and 5% of the sales over $25,000 for the month.

Question

An air conditioning salesperson receives a base salary of $2850 per month plus a commission. The commission is 2% of the sales up to and including $25,000 for the month and 5% of the sales over $25,000 for the month.

a. Write a piecewise function that relates the salesperson total monthly income based off or his/her sales for the month.
b. Determine the salesperson's monthly income if his/her sales were $43,000 for the month.

Answer 1

a. To write a piecewise function that relates the salesperson's total monthly income based on their sales for the month, we can split it into two parts:

Let x represent the sales for the month.

If x ≤ $25,000, the commission is 2% of the sales:
Commission = 0.02 * x

If x > $25,000, the commission is 5% of the sales above $25,000:
Commission = 0.05 * (x - $25,000)

Therefore, the total monthly income can be calculated as:
Total monthly income = Base Salary + Commission

Combining the above information, the piecewise function can be written as:

Total monthly income = $2850 + (0.02 * x) if x ≤ $25,000
Total monthly income = $2850 + (0.05 * (x - $25,000)) if x > $25,000

b. To determine the salesperson's monthly income if their sales were $43,000 for the month, we need to plug in this value in the piecewise function.

For x = $43,000:
Total monthly income = $2850 + (0.05 * ($43,000 - $25,000))
Total monthly income = $2850 + (0.05 * $18,000)
Total monthly income = $2850 + $900
Total monthly income = $3750

Therefore, the salesperson's monthly income, if their sales were $43,000 for the month, would be $3750.

Answer 2

To write a piecewise function that relates the salesperson's total monthly income based on their sales for the month, we need to consider two scenarios: when the sales are up to and including $25,000, and when the sales are over $25,000.

Let's first denote the sales for the month as x.

a. When the sales are up to and including $25,000, the commission rate is 2%. This means for sales up to $25,000, the commission earned would be 2% of the sales.

So, the income from sales up to $25,000 is 0.02 * x.

b. When the sales are over $25,000, the commission rate is 5%. This means for sales over $25,000, the commission earned would be 5% of the sales.

So, the income from sales over $25,000 is 0.05 * (x - 25000).

Now, let's write the piecewise function:

Income(x) =
- (base salary) + (0.02 * x) if x <= 25000
- (base salary) + (0.02 * 25000) + (0.05 * (x - 25000)) if x > 25000

In this case, the base salary is $2850 per month.

b. To determine the salesperson's monthly income if their sales were $43,000 for the month, we can substitute x = 43000 into the piecewise function:

Income(43000) =
- 2850 + (0.02 * 43000) if 43000 <= 25000
- 2850 + (0.02 * 25000) + (0.05 * (43000 - 25000)) if 43000 > 25000

Income(43000) =
- 2850 + 860 if 43000 <= 25000
- 2850 + 500 + 900 if 43000 > 25000

Here, since 43000 is greater than 25000, the second part of the piecewise function applies.

Income(43000) =
- 2850 + 500 + 900
Income(43000) =
$-1450

Therefore, if the salesperson's sales were $43,000 for the month, their monthly income would be -$1450. This means they would have a deficit or loss of $1450 for the month.

An air conditioning salesperson receives a base salary of $2850 per month plus a commission. The commission is 2% of the sales up to and including $25,000 for the month and 5% of the sales over $25,000 for the month.

tum batao

kghkhvkh

a. To write a piecewise function that relates the salesperson's total monthly income based on their sales for the month, we can split it into two parts:

To write a piecewise function that relates the salesperson's total monthly income based on their sales for the month, we need to consider two scenarios: when the sales are up to and including $25,000, and when the sales are over $25,000.