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Capacity-Constrained Break-Even: Is the Target Feasible?

Compare required break-even volume with productive capacity, then rank products by contribution per constrained resource.

By PriceAndProfit Editorial Updated 3 min read

On this page
  1. Worked calculation
  2. Decision checks and limits
  3. Apply the calculation

A mathematical break-even quantity is useful only if the business can produce and sell it within the same period. Capacity can make an otherwise valid formula operationally impossible. Identify the limiting resource, estimate the usable amount available, and compare maximum contribution with fixed costs before treating the calculated sales target as achievable.

Using 120 machine hours gives a $1,000 loss with A alone, $3,000 profit with B alone, or zero with the stated mix.
Hypothetical capacity model. The B-only result requires demand for 800 B units; a capacity plan does not guarantee sales.

Worked calculation

Maximum units = usable constrained resource ÷ resource required per unit; contribution per constrained hour = unit contribution ÷ hours per unit

Suppose a workshop has 120 productive machine hours per month. A product uses 0.3 machine hour per unit, sells for $50, and incurs $30 of variable cost. Capacity is 400 units and contribution is $20 per unit. With $9,000 monthly fixed costs, break-even requires 450 units. The arithmetic is valid for an unconstrained model, but the workshop can produce only 400, yielding $8,000 contribution and a $1,000 operating loss at full capacity.

At the existing 400-unit capacity, required contribution is $9,000 divided by 400, or $22.50 per unit. Holding the $30 variable cost unchanged would require a $52.50 price. This is a feasibility threshold, not evidence of customer acceptance. Alternatively, the original $20 contribution would require 135 productive machine hours for 450 units. Any cost of adding those 15 hours belongs in a revised break-even calculation.

Hypothetical worked example
PlanMachine hoursContributionProfit after $9,000 fixed cost
400 A units 120 $8,000 −$1,000
800 B units if demand exists 120 $12,000 $3,000
200 B plus 300 A 120 $9,000 $0

Decision checks and limits

With multiple products, compare contribution per unit of the constrained resource. Product A might contribute $20 while using 0.3 hour, or approximately $66.6667 per machine hour. Product B might contribute $15 while using 0.15 hour, or $100 per machine hour. B contributes fewer dollars per unit but more per constrained hour. If sufficient B demand exists and there are no other constraints, 120 hours could produce 800 B units and $12,000 contribution.

That ranking alone does not establish the feasible mix. Demand limits, setup time, minimum commitments, and other bottlenecks can change the result. If B demand is only 200 units, it uses 30 hours and contributes $3,000; the remaining 90 hours can produce 300 A units and $6,000 contribution, exactly covering the $9,000 fixed cost. Keep productive hours distinct from calendar or paid hours, and include downtime assumptions explicitly. An infeasible break-even target should remain flagged until a realistic mix, capacity change, price, or cost adjustment resolves the gap.

Apply the calculation

  1. Measure usable capacity

    Subtract planned downtime and setup requirements from available resource hours before translating hours into units.

  2. Calculate the capacity gap

    Show maximum contribution, fixed costs, and any shortfall alongside the unconstrained break-even requirement.

  3. Build a demand-feasible mix

    Allocate constrained time using contribution per resource unit, then check actual demand, sequencing, and other limits before accepting the plan.

Method references: OpenStax: Break-even units and dollars. Accessed October 22, 2026. All dollar figures are hypothetical worked examples.

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