Banaiuka is a company that produces a kind of sweet based on organic bananas. The variable cost of processing a banana and manufacturing the sweet is $5. The fixed annual cost of the banana processing plant and sweet manufacturing is $200. The final price of the Banaiuka's sweet is $30. Thus, the required volume of production in order to break-even is:

Question

Banaiuka is a company that produces a kind of sweet based on organic bananas. The variable cost of processing a banana and manufacturing the sweet is $5. The fixed annual cost of the banana processing plant and sweet manufacturing is $200. The final price of the Banaiuka's sweet is $30. Thus, the required volume of production in order to break-even is:

BlackTom AI · Accepted Answer

Break-even point occurs when total revenue equals total cost, so the number of units q satisfies: price × q = fixed cost + variable cost × q.

1. Relevant knowledge points and concepts
- Fixed cost: cost that does not change with output (here $200).
- Variable cost per unit: cost that varies with each unit produced (here $5 per sweet).
- Selling price per unit: revenue earned per unit (here $30).
- Contribution margin per unit = Selling price − Variable cost. Break-even quantity = Fixed cost / Contribution margin per unit.

2. Step-by-step reasoning
- Compute the contribution margin per unit.
- Set total revenue equal to total cost and solve for q.
- Verify by plugging q back into revenue and total cost.

3. Calculations and intermediate steps
- Contribution margin = 30 − 5 = 25 (dollars per unit).
- Break-even equation: 30q = 200 + 5q.
- Rearranged: 30q − 5q = 200 → 25q = 200.
- Solve for q: q = 200 / 25 = 8.

4. Why the correct answer is correct
- At q = 8: Revenue = 30 × 8 = $240. Total cost = Fixed + Variable = 200 + (5 × 8) = 200 + 40 = $240. Revenue equals total cost, so profit = $0, which is the break-even condition.

5. Why other options are incorrect
- q = 10: Revenue = 300, Total cost = 200 + 50 = 250 → profit = $50 (not break-even).
- q = 3.5: Revenue = 105, Total cost = 200 + 17.5 = 217.5 → loss of $112.5.
- q = 4: Revenue = 120, Total cost = 200 + 20 = 220 → loss of $100.
- "None of the above" is incorrect because an option matching the correct break-even quantity (8) is present.

6. Conclusion
The break-even production volume is 8 units, which matches the provided correct answer: 8.

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