Capacity Constraints in Profit Scenarios

A sales scenario can look profitable while requiring more work than the business can deliver. Capacity constraints should therefore appear inside the model, not as a note added after the profit calculation. Identify the scarce resource first: machine hours, specialist time, packing slots, or another specific bottleneck. Aggregate employee hours may not represent the limiting step.

Compare contribution per constrained hour

Suppose product A contributes $30 per unit and requires two bottleneck hours. Product B contributes $24 per unit and requires one bottleneck hour. A has the higher contribution per unit, but B contributes more per bottleneck hour: $24 compared with A's $15. Assume 100 bottleneck hours are available and demand is limited to 60 units of B and 40 units of A.

Under this simplified model, producing 60 units of B uses 60 hours and contributes $1,440. The remaining 40 hours produce 20 units of A, contributing $600. Total contribution is $2,040 from 100 hours. With $1,800 of fixed costs, modeled operating profit is $240.

Show the cost of ignoring the bottleneck

Producing 40 units of A first uses 80 hours and contributes $1,200. The remaining 20 hours allow 20 units of B, contributing $480. Total contribution is $1,680, leaving a $120 loss after the same fixed costs. The $360 difference follows from the use of constrained hours, not from any change in prices or unit costs.

Meeting all stated demand would require 40 × 2 + 60 × 1 = 140 hours, exceeding capacity by 40 hours. The unconstrained demand plan cannot be presented as deliverable at the existing cost. Any added shift, outside production, or equipment option needs its own incremental cost and feasibility assumptions.

Check the model before applying a ranking

The contribution-per-hour ranking assumes one bottleneck, divisible scheduling at the chosen unit size, stable unit contribution, and no additional restrictions. Setup time, minimum batches, product dependencies, service commitments, and multiple scarce resources can change the feasible mix. Existing customer obligations may also prevent simply favoring the highest contribution product.

Use actual processing times and accepted output, including expected rework where appropriate. A zero time requirement makes this ratio unsuitable for comparing that product on this bottleneck; it does not create infinite productive capacity across the whole business. Keep demand limits visible and test a realistic schedule. The calculation supports a capacity discussion, not a guarantee of profit or an instruction to disregard delivery commitments.

Method references: OpenStax: Break-Even Sensitivity Analysis. Accessed October 22, 2026. All dollar figures are hypothetical worked examples.