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Math  /  Algebra

QuestionQuestion 4 (2 points) Happy Belly Restaurant solls to items: turkey sandwiches and hamburgers. The turkey sandwich accounts for 30%30 \% of their sales revenue, whereas the hamburger accounts for 70%70 \% of their sales revenue. Happy Belly also knows that the margin(\%) of the turkey sandwich is much higher than that of the hamburger: whereas the hamburger's margin(\%) is 20\%, the margin(\%) of the turkey sandwich is 50%50 \%.
Based on this information, Happy Belly wants to understand their break-even revenue. Given that their fixed operating costs per month is $58,000\$ 58,000; how much revenue should the company be making per month to break even? \$200,000 \$290,000 \$150,000 \$100,000

Studdy Solution

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 = (0.3×0.5)+(0.7×0.2) (0.3 \times 0.5) + (0.7 \times 0.2)

STEP 5

Calculate the weighted average margin.
Weighted Average Margin = (0.3×0.5)+(0.7×0.2)=0.15+0.14=0.29 (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 = Fixed CostsWeighted Average Margin\frac{\text{Fixed Costs}}{\text{Weighted Average Margin}}

STEP 7

Solve for the break-even revenue.
Break-even revenue = 58,0000.29\frac{58,000}{0.29}

STEP 8

Calculate the break-even revenue.
Break-even revenue = 58,0000.29≈200,000\frac{58,000}{0.29} \approx 200,000
The break-even revenue is:
200,000\boxed{200,000}

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