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Sagot :
To determine the revised net operating income per month given the different sales volumes, we need to consider the changes in the number of units sold and calculate the impact on the net operating income.
Given data from the problem:
- Sales units: 8,200 units
- Sales per unit: [tex]$30.00 - Variable expenses per unit: $[/tex]19.00
- Contribution margin per unit: [tex]$11.00 - Fixed expenses: $[/tex]54,500
- Net operating income: [tex]$35,700 The contribution margin per unit is the difference between the sales price per unit and the variable expenses per unit: \[ \text{Contribution margin per unit} = \$[/tex]30.00 - \[tex]$19.00 = \$[/tex]11.00 \]
Now let's consider each case independently.
### Case 1: Sales volume increases by 30 units
If the sales volume increases by 30 units, the new sales volume will be:
[tex]\[ \text{New sales volume} = 8,200 + 30 = 8,230 \text{ units} \][/tex]
The new net operating income will be calculated as:
[tex]\[ \text{Revised Net Operating Income} = (\text{New sales volume} \times \text{Contribution margin per unit}) - \text{Fixed expenses} \][/tex]
[tex]\[ \text{Revised Net Operating Income} = (8,230 \times \$11.00) - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$90,530 - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$36,030 \][/tex]
### Case 2: Sales volume decreases by 30 units
If the sales volume decreases by 30 units, the new sales volume will be:
[tex]\[ \text{New sales volume} = 8,200 - 30 = 8,170 \text{ units} \][/tex]
The new net operating income will be calculated as:
[tex]\[ \text{Revised Net Operating Income} = (\text{New sales volume} \times \text{Contribution margin per unit}) - \text{Fixed expenses} \][/tex]
[tex]\[ \text{Revised Net Operating Income} = (8,170 \times \$11.00) - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$89,870 - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$35,370 \][/tex]
### Case 3: Sales volume is 7,200 units
If the sales volume is 7,200 units, the net operating income will be:
[tex]\[ \text{Revised Net Operating Income} = (\text{New sales volume} \times \text{Contribution margin per unit}) - \text{Fixed expenses} \][/tex]
[tex]\[ \text{Revised Net Operating Income} = (7,200 \times \$11.00) - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$79,200 - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$24,700 \][/tex]
The revised net operating incomes for each case are:
[tex]\[ \begin{tabular}{|l|l|} \hline 1. Revised net operating income & \$36,030 \\ \hline 2. Revised net operating income & \$35,370 \\ \hline 3. Revised net operating income & \$24,700 \\ \hline \end{tabular} \][/tex]
Given data from the problem:
- Sales units: 8,200 units
- Sales per unit: [tex]$30.00 - Variable expenses per unit: $[/tex]19.00
- Contribution margin per unit: [tex]$11.00 - Fixed expenses: $[/tex]54,500
- Net operating income: [tex]$35,700 The contribution margin per unit is the difference between the sales price per unit and the variable expenses per unit: \[ \text{Contribution margin per unit} = \$[/tex]30.00 - \[tex]$19.00 = \$[/tex]11.00 \]
Now let's consider each case independently.
### Case 1: Sales volume increases by 30 units
If the sales volume increases by 30 units, the new sales volume will be:
[tex]\[ \text{New sales volume} = 8,200 + 30 = 8,230 \text{ units} \][/tex]
The new net operating income will be calculated as:
[tex]\[ \text{Revised Net Operating Income} = (\text{New sales volume} \times \text{Contribution margin per unit}) - \text{Fixed expenses} \][/tex]
[tex]\[ \text{Revised Net Operating Income} = (8,230 \times \$11.00) - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$90,530 - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$36,030 \][/tex]
### Case 2: Sales volume decreases by 30 units
If the sales volume decreases by 30 units, the new sales volume will be:
[tex]\[ \text{New sales volume} = 8,200 - 30 = 8,170 \text{ units} \][/tex]
The new net operating income will be calculated as:
[tex]\[ \text{Revised Net Operating Income} = (\text{New sales volume} \times \text{Contribution margin per unit}) - \text{Fixed expenses} \][/tex]
[tex]\[ \text{Revised Net Operating Income} = (8,170 \times \$11.00) - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$89,870 - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$35,370 \][/tex]
### Case 3: Sales volume is 7,200 units
If the sales volume is 7,200 units, the net operating income will be:
[tex]\[ \text{Revised Net Operating Income} = (\text{New sales volume} \times \text{Contribution margin per unit}) - \text{Fixed expenses} \][/tex]
[tex]\[ \text{Revised Net Operating Income} = (7,200 \times \$11.00) - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$79,200 - \$54,500 \][/tex]
[tex]\[ \text{Revised Net Operating Income} = \$24,700 \][/tex]
The revised net operating incomes for each case are:
[tex]\[ \begin{tabular}{|l|l|} \hline 1. Revised net operating income & \$36,030 \\ \hline 2. Revised net operating income & \$35,370 \\ \hline 3. Revised net operating income & \$24,700 \\ \hline \end{tabular} \][/tex]
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