Question

An account executive receives a base salary plus a commission. On $20,000 in monthly sales, an account executive would receive compensation of $1500. On $60,000 in monthly sales, an account executive would receive compensation of $2300. Determine a linear function that yields the compensation y of a sales executive for a given amount of monthly sales x.

Use this model to determine the compensation of an account executive who has $100,000 in monthly sales.

Answer 1

Explanation:

To determine the linear function that yields the compensation of a sales executive for a given amount of monthly sales, we can use the two data points provided.

Let's denote the monthly sales as x and the compensation as y.

From the given information, we have two data points:

Data point 1: (20000, 1500)

Data point 2: (60000, 2300)

We can use these two points to determine the equation of the linear function.

The slope of the line can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

Using the values from the data points:

slope = (2300 - 1500) / (60000 - 20000)

= 800 / 40000

= 0.02

The y-intercept of the line can be calculated using the formula:

y-intercept = y - (slope * x)

Using one of the data points, let's use the first data point (20000, 1500):

1500 = 0.02 * 20000 + y-intercept

1500 = 400 + y-intercept

y-intercept = 1500 - 400

y-intercept = 1100

Therefore, the linear function that yields the compensation y of a sales executive for a given amount of monthly sales x is:

y = 0.02x + 1100

This equation represents the relationship between the monthly sales and the compensation, where the coefficient 0.02 represents the increase in compensation per unit increase in monthly sales, and the constant term 1100 represents the base compensation.