Product Mix Optimization Calculator
Enter contribution, resource use, capacity, and demand for two products. The calculator solves the feasible mix with the highest total contribution margin and shows which limits are tight.
Maximum contribution margin$28,800.00
- Recommended Product A quantity
- 300
- Recommended Product B quantity
- 600
- Machine utilization
- 100%
- Unused machine time
- 0
- Labor utilization
- 100%
- Unused labor time
- 0
- Binding constraints
- Machine time, Labor time
- Value of one extra machine minute
- $1.20
- Value of one extra labor minute
- $1.20
Unit contribution margin is $36.00 for Product A and $30.00 for Product B.
Fractional quantities are allowed; round only after checking capacity and demand again.
How to use this calculator
- Enter each product selling price and variable cost to set the contribution margin per unit.
- Enter the machine and labor minutes each unit uses.
- Enter the most units demand will absorb for each product.
- Enter the machine and labor minutes available for the same planning period.
- Review the recommended mix, slack, binding constraints, and marginal value of extra capacity.
How the product mix is calculated
This calculator treats the decision as a two-product linear program. Product A quantity is x and Product B quantity is y. Unit contribution margin is selling price minus variable cost, so cA = pA - vA and cB = pB - vB.
The objective is:
maximize Z = cA × x + cB × y
The plan must stay within the entered limits:
mA × x + mB × y <= Mfor machine minutes.lA × x + lB × y <= Lfor labor minutes.0 <= x <= dAand0 <= y <= dBfor demand.
For two products, the best feasible answer occurs at a corner of the feasible region. The calculator evaluates every intersection of the boundary lines for zero production, demand limits, machine capacity, and labor capacity. It keeps the points that satisfy every constraint, computes total contribution margin at each point, and returns the point with the largest value.
Why contribution margin matters
A product with the highest selling price is not always the best use of constrained capacity. The relevant amount is the selling price left after variable costs, because fixed costs are assumed not to change between feasible mixes. When only one resource is scarce, contribution margin per unit of that limiting factor can rank products well. With two constrained resources, that shortcut can fail because the best answer depends on how the two products use both resources together.
Binding limits and unused capacity
A binding constraint has zero slack at the recommended mix. If machine time is binding, all available machine minutes are used. If Product B demand is binding, the plan would sell the maximum Product B units entered. Nonbinding limits have slack, which means that limit is not holding back contribution margin at the current optimum.
The value of one extra machine or labor minute is computed by solving the optimization again with one additional minute of that resource. This is a local marginal value. It can drop to zero after another resource or a demand limit becomes binding.
What this calculator leaves out
The model assumes divisible units, constant selling prices, constant variable costs, and steady resource use over the planning range. It does not include setup sequencing, batch sizes, changeover time, minimum production commitments, supplier risk, customer strategy, or fixed overhead changes. Use the answer as an operating estimate, then test any rounded schedule against the same capacity and demand limits.
Worked example
Suppose Product A sells for $80, has $44 of variable cost, uses 20 machine minutes and 10 labor minutes, and has demand for 500 units. Product B sells for $65, has $35 of variable cost, uses 10 machine minutes and 15 labor minutes, and has demand for 700 units. With 12,000 machine minutes and 12,000 labor minutes available, contribution margins are $36 for A and $30 for B.
The optimum is 300 units of Product A and 600 units of Product B. That mix uses 12,000 machine minutes and 12,000 labor minutes, so both resource constraints bind. Total contribution margin is 300 × $36 + 600 × $30 = $28,800. One more machine minute or labor minute is worth about $1.20 at this point, until another constraint changes the optimum.
Common questions
How do I calculate the optimal product mix with two limiting factors?
Set up each product quantity as a decision variable, write the machine, labor, and demand limits as constraints, then maximize total contribution margin. With two products, the optimum is found by checking feasible corner points created by those constraint lines.
Why use contribution margin instead of sales price?
Sales price ignores the variable cost required to make each unit. Contribution margin measures the amount each unit adds toward fixed costs and profit, which is the amount that changes when the production mix changes.
What does a binding constraint mean?
A binding constraint has no unused capacity at the recommended mix. It is one of the limits holding back the objective, although its marginal value can still be zero if another binding limit prevents any better use of added capacity.
Why can contribution per machine hour give the wrong answer?
That ranking works only when one resource is the real bottleneck. When machine time and labor time are both limited, a product that looks best on machine time may consume too much labor, so the best mix has to consider both constraints together.
Should fixed manufacturing overhead be included?
Usually no. The constrained-resource contribution-margin method excludes fixed costs unless they change between the alternatives being compared. Include only costs that vary with the units in the plan.