https://file.aiquickdraw.com/mathbot/file/1726346592894h0un6ioh.jpg

To solve for the net operating income (NOI) given the data in the image, I will need to work through the relevant values. Based on the problem, it seems that you are given information about costs and commissions, and you're asked to calculate NOI with a slight modification to the commission structure.

Here's the approach:

### **Key Data:**
- **Selling price per unit**: $30.00
- **Variable expenses per unit**:
  - Invoice cost: $9.50
  - Sales commission: $5.50
  - Total variable expenses: $15.00
- **Fixed expenses**:
  - Advertising: $36,000
  - Rent: $23,000
  - Salaries: $130,000
  - **Total fixed expenses**: $189,000
- **Number of shoes sold**: 15,700 pairs
- **New sales commission**: $0.50 per pair sold over the break-even point

### **Steps to Solve for Net Operating Income:**

1. **Contribution Margin per Pair**:
   The contribution margin is the selling price minus the total variable expenses.
   \[
   \text{Contribution Margin} = 30 - 15 = 15 \, \text{(per pair)}
   \]

2. **Break-even Point in Units**:
   The break-even point is calculated by dividing the total fixed expenses by the contribution margin per unit.
   \[
   \text{Break-even point (units)} = \frac{\text{Total fixed expenses}}{\text{Contribution margin per unit}} = \frac{189,000}{15} = 12,600 \, \text{pairs}
   \]

3. **Units Sold Above Break-even**:
   You sold 15,700 pairs, and the break-even point is 12,600 pairs.
   \[
   \text{Excess units sold} = 15,700 - 12,600 = 3,100 \, \text{pairs}
   \]

4. **Effect of New Commission**:
   You are now paying an additional $0.50 commission for each pair sold over the break-even point.
   \[
   \text{Additional commission cost} = 3,100 \times 0.50 = 1,550
   \]

5. **New Total Variable Expenses**:
   The total variable expenses now include the additional commission, so:
   \[
   \text{Total Variable Expenses} = 15 \times 15,700 + 1,550 = 235,500 + 1,550 = 237,050
   \]

6. **Total Revenue**:
   \[
   \text{Total Revenue} = 30 \times 15,700 = 471,000
   \]

7. **Net Operating Income**:
   \[
   \text{NOI} = \text{Total Revenue} - \text{Total Variable Expenses} - \text{Fixed Expenses} = 471,000 - 237,050 - 189,000 = 44,950
   \]

So, the corrected **Net Operating Income** would be **$44,950**.

Let me know if you would like further details or have any questions!

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Here are 5 related questions to expand on this topic:
1. What happens to NOI if the selling price increases by $2 per unit?
2. How would the break-even point change if fixed costs were reduced by $10,000?
3. What is the impact of increasing the sales commission to $1 per pair sold over break-even?
4. How does the break-even point change if the variable costs increase by $1 per unit?
5. What happens to the contribution margin if the selling price remains the same but variable expenses decrease?

**Tip:** Always verify the accuracy of your contribution margin calculation as it directly impacts both the break-even point and the net operating income.

What will be Shop 48's net operating income (loss) if 15,700 pairs of shoes are sold and a 50-cent commission is paid on each pair sold in excess of the break-even point?

Calculate the net operating income for Shop 48, based on selling 15,700 pairs of shoes with a $30 selling price, $15 variable expenses per pair, and a 50-cent commission for shoes sold beyond the break-even point of 12,600 pairs. Learn step-by-step how to analyze fixed and variable costs, determine the break-even point, and compute NOI.

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