To determine who had the largest dollar amount in sales for the month of January, we need to calculate the sales for each employee type based on their earnings and commission structures.
### 1. Salary Plus Commission Employee
- Earnings: [tex]$3.5 thousand
- Base Salary: $[/tex]2000
- Commission Rate: 3%
First, we convert the earnings into dollars:
[tex]\[ 3.5 \times 1000 = 3500 \text{ dollars} \][/tex]
Next, we isolate the commission earned by subtracting the base salary from the total earnings:
[tex]\[ 3500 - 2000 = 1500 \text{ dollars earned from commission} \][/tex]
Finally, we calculate the total sales by dividing the commission earned by the commission rate:
[tex]\[ \frac{1500}{0.03} = 50000 \text{ dollars in sales} \][/tex]
### 2. Straight Commission Employee
- Earnings: [tex]$3.85 thousand
- Commission Rate: 7%
First, convert the earnings into dollars:
\[ 3.85 \times 1000 = 3850 \text{ dollars} \]
Next, calculate the total sales by dividing the earnings by the commission rate:
\[ \frac{3850}{0.07} = 55000 \text{ dollars in sales} \]
### 3. Graduated Commission Employee
- Earnings: $[/tex]3.6 thousand
- Commission Rates: 5% on the first [tex]$40,000, 8% on amounts over $[/tex]40,000
First, convert the earnings into dollars:
[tex]\[ 3.6 \times 1000 = 3600 \text{ dollars} \][/tex]
Now, let's determine if the total commission falls entirely within the 5% bracket or if it exceeds into the 8% bracket.
Calculate the commission if the sales were exactly [tex]$40,000:
\[ 40000 \times 0.05 = 2000 \text{ dollars} \]
Since the earnings ($[/tex]3600) exceed [tex]$2000, there must be additional sales beyond $[/tex]40,000. Therefore, we need to calculate the additional earnings that came from the 8% bracket:
[tex]\[ 3600 - 2000 = 1600 \text{ dollars from the 8% bracket} \][/tex]
Now, find out how much sales resulted from the 8% commission:
[tex]\[ \frac{1600}{0.08} = 20000 \text{ dollars} \][/tex]
The total sales are the sum of the sales from the 5% bracket and 8% bracket:
[tex]\[ 40000 + 20000 = 60000 \text{ dollars in sales} \][/tex]
### Conclusion
By comparing the total sales for each employee:
- Salary Plus Commission Employee: [tex]$50,000
- Straight Commission Employee: $[/tex]55,000
- Graduated Commission Employee: $60,000
The largest dollar amount in sales for the month of January is by the Graduated Commission Employee.
Therefore, the correct answer is:
c. The graduated commission employee.
