Use the information from Exercise 28 to answer the following...

Use the information from Exercise 28 to answer the following questions. a. If the salesperson is given a raise by increasing the guaranteed pay per week $\$ 150,$ how would that change the equation found in Exercise 28 part a? b. If instead of raising the guaranteed pay per week, the salesperson's commission rate was increased from $5 \%$ to $6 \%,$ how would that change the equation found in Exercise 27 part a? c. If the salesperson makes an average of $\$ 20,000$ in sales per week, which raise would be best for the salesperson? d. If the salesperson makes an average of $\$ 11,000$ in sales per week, which raise would be best for the company? e. What amount of sales per week would make these raises result in the same weekly pay?

Use the information from Exercise 28 to answer the following questions.
a. If the salesperson is given a raise by increasing the guaranteed pay per week $\$ 150,$ how would that change the equation found in Exercise 28 part a?
b. If instead of raising the guaranteed pay per week, the salesperson's commission rate was increased from $5 \%$ to $6 \%,$ how would that change the equation found in Exercise 27 part a?
c. If the salesperson makes an average of $\$ 20,000$ in sales per week, which raise would be best for the salesperson?
d. If the salesperson makes an average of $\$ 11,000$ in sales per week, which raise would be best for the company?
e. What amount of sales per week would make these raises result in the same weekly pay?

Key Concepts

Base Salary (Guaranteed Pay)

The base salary, also known as guaranteed pay, is the fixed amount received regardless of sales performance. This steady income provides a security layer in the compensation structure and, when increased, linearly raises the overall weekly earnings independent of the variable commission rate.

Break-even Analysis

Break-even analysis involves determining the sales volume at which different compensation schemes result in the same earnings. By equating the earnings from a higher base salary with those from a higher commission rate, one can solve for the point where both pay strategies yield equal income, aiding in decision-making for both the salesperson and the company.

Linear Functions

Linear functions are mathematical expressions that represent relationships where the change in one variable is directly proportional to the change in another. In real-world contexts like salary calculations, the total pay is expressed as a function combining a fixed component (base salary) with a variable component (commission on sales), forming a straight-line graph when plotted.

Commission

Commission is the percentage-based component of a salesperson's pay. It is calculated by applying a set rate to the total amount of sales, meaning that higher sales volumes directly increase the commission earnings, making it a crucial part of the overall compensation model.

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