Question

A sales agent is given a choice of two different compensation plans. The first plan has no salary, but a $10 \%$ commission on total sales. The second plan has a salary of $\$ 3000$ per month, plus a $2 \%$ commission on total sales. What range of monthly sales will make the first plan a better choice for the sales agent?

Name: Problem 55, Chapter 4: Contemporary Precalculus
Uploaded: 2020-07-22T12:59:20-08:00
Duration: 1 min 27 s
Channel: Charles Carter
Description: A sales agent is given a choice of two different compensation plans. The first plan has no salary, but a 10 % commission on total sales. The second plan has a salary of 3000 per month, plus a 2 % commission on total sales. What range of monthly sales will make the first plan a better choice for the sales agent?

   A sales agent is given a choice of two different compensation plans. The first plan has no salary, but a $10 \%$ commission on total sales. The second plan has a salary of $\$ 3000$ per month, plus a $2 \%$ commission on total sales. What range of monthly sales will make the first plan a better choice for the sales agent?

Contemporary Precalculus

Thomas W.… 5th Edition

Chapter 4, Problem 55

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Solved by Expert Charles Carter

07/22/2020

Step 1

For the first plan, the sales agent gets 10% of all sales as their salary. This can be represented as $0.10s$, where $s$ is the total sales. Show more…

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A sales agent is given a choice of two different compensation plans. The first plan has no salary, but a $10 \%$ commission on total sales. The second plan has a salary of $\$ 3000$ per month, plus a $2 \%$ commission on total sales. What range of monthly sales will make the first plan a better choice for the sales agent?

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Key Concepts

Break-even Analysis

Break-even analysis involves finding the point at which two different financial options yield the same result. Once this point is identified, it is possible to determine which option is more advantageous once the variable (such as sales) exceeds the break-even point.

Compensation Structures

Compensation structures typically combine fixed pay components and variable pay components such as commissions. Understanding how fixed salaries interact with performance-based commissions is essential in evaluating and comparing different pay plans in a business context.

Linear Inequalities

Linear inequalities are used to model relationships where one expression is greater than or less than another. In problems comparing different compensation plans, they allow us to determine the conditions under which one plan yields a higher total than the other by solving for the variable (in this case, total sales).

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