Answer :
To determine which employee did not have the same dollar amount in sales for the month of February as the other employees, we need to calculate the total sales for each employee based on their earnings and their respective commission structures. Given the earnings for February, we carry out the following calculations:
1. Employee #1:
- Earnings: [tex]$4.7 thousand - Commission Structure: $[/tex]2,000 + 3% on all sales
To find the total sales, we first subtract the fixed component of the earnings which is [tex]$2,000. The remaining earnings come from the 3% commission. Therefore: \[ \text{Total Sales} = \frac{\text{Earnings} - 2000}{0.03} \] Given the earnings were $[/tex]4,700:
[tex]\[ \text{Total Sales} = \frac{4700 - 2000}{0.03} = 90,000 \][/tex]
2. Employee #2:
- Earnings: [tex]$4.9 thousand - Commission Structure: 7% on all sales To find the total sales, we divide the earnings by the commission rate: \[ \text{Total Sales} = \frac{\text{Earnings}}{0.07} \] Given the earnings were $[/tex]4,900:
[tex]\[ \text{Total Sales} = \frac{4900}{0.07} = 70,000 \][/tex]
3. Employee #3:
- Earnings: [tex]$4.4 thousand - Commission Structure: 5% on the first $[/tex]40,000 + 8% on anything over [tex]$40,000 To find the total sales, we need to consider the two-tier commission structure. First, we need to determine whether the total sales are below or above $[/tex]40,000 based on the earnings:
If the earnings from sales below [tex]$40,000 exceed the employee's earnings: \[ \text{Earnings if all sales are below $[/tex]\[tex]$40,000$[/tex]} = 0.05 \times 40,000 = 2,000
\]
Since the earnings [tex]$4,400$[/tex] are greater than [tex]$2,000, Employee #3 has some sales above $[/tex]40,000.
Total earnings are split into two parts:
[tex]\[ \text{Earnings from $\$40,000$ sales} = 0.05 \times 40,000 = 2,000 \][/tex]
[tex]\[ \text{Earnings from sales over $\$40,000$} = 4,400 - 2,000 = 2,400 \][/tex]
The sales for additional earnings beyond [tex]$40,000: \[ \text{Additional Sales} = \frac{2,400}{0.08} = 30,000 \] Total sales for Employee #3: \[ \text{Total Sales} = 40,000 + 30,000 = 70,000 \] From the calculations: - Employee #1 had total sales of \$[/tex]90,000.
- Employee #2 had total sales of \[tex]$70,000. - Employee #3 had total sales of \$[/tex]70,000.
We see that Employee #1 did not have the same dollar amount in sales for the month of February as Employee #2 and Employee #3. Hence, the correct answer is:
a. Employee \#1
1. Employee #1:
- Earnings: [tex]$4.7 thousand - Commission Structure: $[/tex]2,000 + 3% on all sales
To find the total sales, we first subtract the fixed component of the earnings which is [tex]$2,000. The remaining earnings come from the 3% commission. Therefore: \[ \text{Total Sales} = \frac{\text{Earnings} - 2000}{0.03} \] Given the earnings were $[/tex]4,700:
[tex]\[ \text{Total Sales} = \frac{4700 - 2000}{0.03} = 90,000 \][/tex]
2. Employee #2:
- Earnings: [tex]$4.9 thousand - Commission Structure: 7% on all sales To find the total sales, we divide the earnings by the commission rate: \[ \text{Total Sales} = \frac{\text{Earnings}}{0.07} \] Given the earnings were $[/tex]4,900:
[tex]\[ \text{Total Sales} = \frac{4900}{0.07} = 70,000 \][/tex]
3. Employee #3:
- Earnings: [tex]$4.4 thousand - Commission Structure: 5% on the first $[/tex]40,000 + 8% on anything over [tex]$40,000 To find the total sales, we need to consider the two-tier commission structure. First, we need to determine whether the total sales are below or above $[/tex]40,000 based on the earnings:
If the earnings from sales below [tex]$40,000 exceed the employee's earnings: \[ \text{Earnings if all sales are below $[/tex]\[tex]$40,000$[/tex]} = 0.05 \times 40,000 = 2,000
\]
Since the earnings [tex]$4,400$[/tex] are greater than [tex]$2,000, Employee #3 has some sales above $[/tex]40,000.
Total earnings are split into two parts:
[tex]\[ \text{Earnings from $\$40,000$ sales} = 0.05 \times 40,000 = 2,000 \][/tex]
[tex]\[ \text{Earnings from sales over $\$40,000$} = 4,400 - 2,000 = 2,400 \][/tex]
The sales for additional earnings beyond [tex]$40,000: \[ \text{Additional Sales} = \frac{2,400}{0.08} = 30,000 \] Total sales for Employee #3: \[ \text{Total Sales} = 40,000 + 30,000 = 70,000 \] From the calculations: - Employee #1 had total sales of \$[/tex]90,000.
- Employee #2 had total sales of \[tex]$70,000. - Employee #3 had total sales of \$[/tex]70,000.
We see that Employee #1 did not have the same dollar amount in sales for the month of February as Employee #2 and Employee #3. Hence, the correct answer is:
a. Employee \#1
