To determine who had the largest dollar amount in sales for the month of December, let's analyze each employee's earnings and find out their corresponding sales.
1. Salary plus commission employee:
- Earnings: [tex]$4.4$[/tex] thousand
- Formula: [tex]$Earnings = \$[/tex]2,000 + 3\%[tex]$ on all sales
\[ 4.4\text{ (in thousands)} = 2 + 0.03 \times \text{Sales} \]
Solving for Sales:
\[ 4.4 - 2 = 0.03 \times \text{Sales} \]
\[ 2.4 = 0.03 \times \text{Sales} \]
\[ \text{Sales} = \frac{2.4}{0.03} \]
\[ \text{Sales} = 80 \text{ (in thousands)} \]
2. Straight commission employee:
- Earnings: $[/tex]5.6[tex]$ thousand
- Formula: $[/tex]7\%[tex]$ on all sales
\[ 5.6\text{ (in thousands)} = 0.07 \times \text{Sales} \]
Solving for Sales:
\[ \text{Sales} = \frac{5.6}{0.07} \]
\[ \text{Sales} = 80 \text{ (in thousands)} \]
3. Graduated commission employee:
- Earnings: $[/tex]5.2[tex]$ thousand
- Formula: $[/tex]5\%[tex]$ on the first $[/tex]40,000 + 8\%[tex]$ on anything over $[/tex]40,000[tex]$
Let $[/tex]X[tex]$ be the amount of sales over $[/tex]40,000.
[tex]\[ 5.2 \text{ (in thousands)} = 0.05 \times 40000 + 0.08 \times X \][/tex]
This can be written as:
[tex]\[ 5.2 = 2 + 0.08 \times X \][/tex]
[tex]\[ 5.2 - 2 = 0.08 \times X \][/tex]
[tex]\[ 3.2 = 0.08 \][/tex]
[tex]\[ X = \frac{3.2}{0.08} \][/tex]
[tex]\[ X = 40 \text{ (in thousands)} \][/tex]
Therefore, the total sales would be:
[tex]\[ 40000 + X = 40000 + 40000 = 80000 + 12000 = 15065 \text{ (in thousands)} \][/tex]
Comparing the sales figures:
- Salary plus commission employee: [tex]$80 \text{ thousand}$[/tex]
- Straight commission employee: [tex]$80 \text{ thousand}$[/tex]
- Graduated commission employee: [tex]$15065 \text{ thousand}$[/tex]
Therefore, the graduated commission employee had the largest dollar amount in sales for the month of December.
c. The graduated commission employee is the best answer.
