To solve this problem, let's calculate the sales amounts for each employee in February based on their earnings and commission structures.
### Employee \#1:
- Earnings: [tex]$4.7 \times 1000 = \$[/tex]4700[tex]$
- Commission Structure: \$[/tex]2000 base salary + 3% of sales
First, we calculate the part of the earnings that comes from the commission:
[tex]\[ \text{Commission earnings} = \$4700 - \$2000 = \$2700 \][/tex]
Next, we find the total sales [tex]\( S \)[/tex] using the 3% commission rate:
[tex]\[ 0.03 \times S = \$2700 \][/tex]
[tex]\[ S = \frac{\$2700}{0.03} \][/tex]
[tex]\[ S = \$90,000 \][/tex]
### Employee \#2:
- Earnings: [tex]$4.9 \times 1000 = \$[/tex]4900[tex]$
- Commission Structure: 7% of all sales
We find the total sales \( S \) using the 7% commission rate:
\[ 0.07 \times S = \$[/tex]4900 \]
[tex]\[ S = \frac{\$4900}{0.07} \][/tex]
[tex]\[ S = \$70,000 \][/tex]
### Employee \#3:
- Earnings: [tex]$4.4 \times 1000 = \$[/tex]4400[tex]$
- Commission Structure: 5% on the first \$[/tex]40,000 + 8% on anything over \[tex]$40,000
First, we calculate the earnings from the first \$[/tex]40,000:
[tex]\[ \text{Earnings from first \$40,000} = 0.05 \times \$40,000 = \$2000 \][/tex]
Next, we calculate the remaining earnings:
[tex]\[ \text{Remaining Earnings} = \$4400 - \$2000 = \$2400 \][/tex]
The remaining earnings come from sales over \[tex]$40,000:
\[ 0.08 \times \text{Sales over \$[/tex]40,000} = \[tex]$2400 \]
\[ \text{Sales over \$[/tex]40,000} = \frac{\[tex]$2400}{0.08} \]
\[ \text{Sales over \$[/tex]40,000} = \[tex]$30,000 \]
The total sales are:
\[ S = \$[/tex]40,000 + \[tex]$30,000 = \$[/tex]70,000 \]
### Summary of Sales:
- Employee \#1: \[tex]$90,000
- Employee \#2: \$[/tex]70,000
- Employee \#3: \$70,000
Based on the calculations, Employee \#1 had a different sales amount compared to Employee \#2 and Employee \#3.
Thus, the employee who did not have the same dollar amount in sales for the month of February as the other two employees is:
a. Employee \#1.
