In a manufacturing operation, the break-even point (BEP) is reached when which condition holds true?

Introduction / Context:
Break-even analysis is a staple of plant economics, revealing the sales volume where neither profit nor loss occurs. This helps set pricing, capacity utilization, and risk thresholds for chemical plants.

Given Data / Assumptions:

• Single product or equivalent product-mix with linear costs and revenues in the relevant range.
• Fixed and variable costs are identifiable.

Concept / Approach:
At BEP, total revenue equals total cost. Profit is zero and contribution just covers fixed costs. Any additional unit sold beyond BEP generates profit equal to its contribution margin.

Step-by-Step Solution:
1) Define: Total cost = fixed cost + variable cost.2) At BEP: total revenue = total cost, so profit = 0.3) Therefore, the condition is total annual product cost equals total annual sales.

Verification / Alternative check:
Graphical BEP shows the intersection of total cost and total revenue lines at the break-even output level.

Why Other Options Are Wrong:
(a) Production rate equality to an assigned value is arbitrary and unrelated to BEP.
(c) Profit equals budgeted value is not the BEP definition.
(d) Sales equal fixed cost ignores variable cost recovery, which must also be covered at BEP.
(e) Contribution margin cannot be zero at BEP; contribution equals fixed cost at BEP.

Common Pitfalls:
Ignoring variable cost coverage at BEP; confusing cash break-even with accounting break-even.

Final Answer:
Total annual product cost equals total annual sales (revenue)