Math Snap

STEP 1

1. Happy Belly Restaurant sells two items: turkey sandwiches and hamburgers.
2. Turkey sandwiches account for 30% of sales revenue.
3. Hamburgers account for 70% of sales revenue.
4. The margin for turkey sandwiches is 50%.
5. The margin for hamburgers is 20%.
6. Fixed operating costs per month are $58,000.
7. We need to find the break-even revenue.

STEP 2

1. Define the break-even point.
2. Calculate the weighted average margin.
3. Set up the break-even equation.
4. Solve for the break-even revenue.

STEP 3

Define the break-even point. The break-even point is when total revenue equals total costs (fixed costs + variable costs). In this case, we want the revenue to cover the fixed operating costs.

STEP 4

Calculate the weighted average margin. The weighted average margin is calculated based on the percentage of revenue each product contributes and their respective margins.
Weighted Average Margin = $(0.3 \times 0.5) + (0.7 \times 0.2)$

STEP 5

Calculate the weighted average margin.
Weighted Average Margin = $(0.3 \times 0.5) + (0.7 \times 0.2) = 0.15 + 0.14 = 0.29$ or 29%

STEP 6

Set up the break-even equation. The break-even revenue is when the weighted average margin covers the fixed costs.
Break-even revenue = $\frac{\text{Fixed Costs}}{\text{Weighted Average Margin}}$

STEP 7

Solve for the break-even revenue.
Break-even revenue = $\frac{58,000}{0.29}$

Calculate the break-even revenue.
Break-even revenue = $\frac{58,000}{0.29} \approx 200,000$
The break-even revenue is:
$\boxed{200,000}$