To determine who had the largest dollar amount in sales for the month of January, we need to analyze the given earnings for each type of commission and calculate the sales corresponding to these earnings. The three types of commissions given are:
1. Salary plus commission: \[tex]$2,000 plus 3% on all sales.
2. Straight commission: 7% on all sales.
3. Graduated commission: 5% on the first \$[/tex]40,000 plus 8% on anything over \[tex]$40,000.
Let's determine the sales for each type of commission based on the January earnings.
### 1. Salary plus commission:
The earnings for January are \$[/tex]3.5k (or \[tex]$3,500).
Using the formula:
\[
\$[/tex]3,500 = \[tex]$2,000 + 0.03 \times \text{sales}
\]
Solve for sales:
\[
\$[/tex]1,500 = 0.03 \times \text{sales}
\]
[tex]\[
\text{sales} = \frac{\$1,500}{0.03} = \$50,000
\][/tex]
### 2. Straight commission:
The earnings for January are \[tex]$3.85k (or \$[/tex]3,850).
Using the formula:
[tex]\[
\$3,850 = 0.07 \times \text{sales}
\][/tex]
Solve for sales:
[tex]\[
\text{sales} = \frac{\$3,850}{0.07} = \$55,000
\][/tex]
### 3. Graduated commission:
The earnings for January are \[tex]$3.6k (or \$[/tex]3,600).
Using the formula:
[tex]\[
\$3,600 = 0.05 \times \$40,000 + 0.08 \times (\text{sales} - \$40,000)
\][/tex]
Solve for sales:
[tex]\[
\$3,600 = \$2,000 + 0.08 \times (\text{sales} - \$40,000)
\][/tex]
[tex]\[
\$1,600 = 0.08 \times (\text{sales} - \$40,000)
\][/tex]
[tex]\[
\text{sales} - \$40,000 = \frac{\$1,600}{0.08} = \$20,000
\][/tex]
[tex]\[
\text{sales} = \$40,000 + \$20,000 = \$60,000
\][/tex]
### Comparison:
- Salary plus commission sales: \[tex]$50,000
- Straight commission sales: \$[/tex]55,000
- Graduated commission sales: \[tex]$60,000
The largest dollar amount in sales for January is \$[/tex]60,000, which was achieved by the graduated commission employee.
Answer:
c. The graduated commission employee.
