Product mix decision practice compares every feasible whole-unit choice under supplied capacity and demand limits. Save the alternatives, best contribution and reason, without treating contribution as net profit or the assumed sales as a forecast.
Content last updated: 17 October 2026.
What does a product mix decision actually choose?
A product mix decision chooses quantities of different products within a stated planning boundary. This exercise leaves you with every feasible whole-unit alternative, its contribution and the reason for the best result. It does not approve a factory schedule, predict demand or tell a real business what to sell.
Imagine an independent workshop comparing two decorative items that use the same scarce machine capacity. A high price, a large contribution per item and a high contribution per resource unit are different observations. None should silently replace the objective and constraints you were given.
Keep this separate from the break-even calculation, which asks how much selling covers the costs included in a period. Here the capacity budget is supplied and the question is which feasible quantities produce the largest stated contribution. The amount of fixed cost is not being calculated.
Contribution means selling price less the variable costs included for that unit. It is money available toward fixed expenses, not net profit. The profit margin guide addresses other profit measures. Our narrow purpose is a transparent comparison, not an accounting report or a promise of increased earnings.
Preserve the supplied two-product contract
Use fictional money units and resource units for one frozen planning period. Only whole items are allowed. Each product can be selected in quantities zero through three. Producing nothing is permitted. Every selected unit up to the stated demand ceiling is stipulated sold; this is a teaching assumption, not a verified customer forecast.
For A, price is eight, variable cost five and resource use four per unit. For B, price is six, variable cost four and resource use three. Start with total resource capacity six. Do not change a price or assume an extra buyer to improve a disappointing result.
| Product | Price | Variable cost | Contribution/unit | Resource/unit | Demand cap |
|---|---|---|---|---|---|
| A | 8 | 5 | 3 | 4 | 3 |
| B | 6 | 4 | 2 | 3 | 3 |
Fixed expenses stay unchanged across the alternatives. There are no previous commitments, setup costs, minimum batches, losses, product interactions or other constrained resources. These omissions are explicit boundaries. If they matter in a real workshop, the result below is not a complete operating decision.
The new commitment check protects existing orders and applies a supplied priority rule. This exercise does not invent such a priority. Both quantities are optional and the contribution objective is provided before comparing alternatives. Customer rights, quality and delivery obligations cannot be inferred from the arithmetic.
List every feasible whole-unit alternative before choosing
Let a denote the count of A and b the count of B. Each is an integer from zero to three. Resource use is 4a+3b and must not exceed six. Total contribution is 3a+2b. First reject combinations that violate the resource or demand limits; only then compare their objective values.
With no A, you can choose zero, one or two B. Three B would consume nine and is infeasible. With one A, four units are consumed and two remain, insufficient for a B. Two A already need eight, so every row containing two or three A is outside the original capacity.
That exhausts the choices rather than sampling attractive rows. Keep the zero-production row visible. Unused capacity is simply the part not consumed in this model; it is not another product, a cash balance or an assumed resource carried into a later period.
| A | B | Used | Unused | Contribution |
|---|---|---|---|---|
| 0 | 0 | 0 | 6 | 0 |
| 0 | 1 | 3 | 3 | 2 |
| 0 | 2 | 6 | 0 | 4 |
| 1 | 0 | 4 | 2 | 3 |
Check each row twice. Multiply quantities by resource use, add them and subtract from capacity. Separately multiply quantities by contribution per unit and add those amounts. Mixing resource and money columns makes a plausible-looking table meaningless.
Exhaustive listing is practical because the domain is deliberately tiny. This is not a general claim that manually listing every possibility will be manageable for a large catalog or a multi-resource factory. The benefit is that somebody else can see exactly which choices your claim considered.
Explain why the two-B mix wins this comparison
The four feasible contribution values are zero, two, four and three. The largest is four, achieved only by zero A and two B. This uses all six resource units. No other original feasible mix ties it under the supplied objective.
Do not summarize that result as “B is always better.” A contributes three per item and B contributes two. Whole-item fit within this particular capacity budget changes the choice. Altering capacity, demand, prices or costs requires a new feasible set and a fresh comparison.
The selected B units are not actual sales. Their sale is stipulated only for this practice. Four is not net profit because fixed expenses and any other excluded charges have not been deducted. If an alternative changes fixed costs, contribution alone may no longer preserve the relevant ranking.
The kit capacity plan asks how many identical complete sets a fixed recipe supports. Our decision is different: choose between quantities of different products under one explicit objective. Neither exercise authorizes a stock movement, purchase or customer commitment.
Why can taking the best ratio first lose?
A contributes three for four resource units, a ratio of 3/4. B contributes two for three, a ratio of 2/3. Compare exactly: three times three is nine, while two times four is eight, so A has the higher ratio. No rounded decimal is needed to decide the ordering.
Now define the shortcut precisely: take as many whole A as fit, then fill any remaining capacity with whole B, respecting demand caps. At capacity six it takes one A, uses four and leaves two. Neither a B nor another A fits. Contribution stops at three. Our complete feasible table contains two B with contribution four, so this shortcut misses the best whole-unit result here.
This is a demonstrated counterexample, not a claim that ratios are useless or that every accounting reference is wrong. The opened conceptual sources explain comparisons involving scarce resources. They do not validate every possible indivisible small set. Our claim rests on complete enumeration. ACCA distinguishes materials-only throughput from contribution. This exercise deducts the supplied total variable cost, not materials alone.
If using AI for formatting, ask for all feasible integer pairs and the constraint check, not just a product ranking. Then compare its answer with the four rows yourself. The artificial intelligence guide covers broader tool use; no account is required to complete this manual task.
Optional sensitivity: more capacity can produce a tie
Change only capacity from six to nine. Keep both prices, both variable costs, resource requirements and demand ceilings unchanged. Preserve the original calculation and create a separate scenario. Its complete seven-row feasible set appears below; this extension is optional after the smaller core exercise.
| A | B | Used | Unused | Contribution |
|---|---|---|---|---|
| 0 | 0 | 0 | 9 | 0 |
| 0 | 1 | 3 | 6 | 2 |
| 0 | 2 | 6 | 3 | 4 |
| 0 | 3 | 9 | 0 | 6 |
| 1 | 0 | 4 | 5 | 3 |
| 1 | 1 | 7 | 2 | 5 |
| 2 | 0 | 8 | 1 | 6 |
The maximum contribution is six, achieved by both zero A with three B and two A with zero B. The first consumes nine resource units. The second consumes eight and leaves one unused. Neither is worse under the stated contribution objective merely because its utilization differs.
Report both winners. A preference for using every resource unit, serving a named customer or avoiding an imagined setup is not part of the supplied objective. If the owner wants a secondary rule, record that as another question rather than quietly inventing an answer.
There is a compact independent boundary check. With A fixed at zero, at most three B fit and contribute six. With A fixed at one, at most one B fits and total contribution is five. With A fixed at two, B must be zero and contribution is six. Three A cannot fit. Because each additional feasible B adds two, the largest feasible B is best for each fixed A. These boundaries independently recover every tied winner.
Save the decision, limits and unanswered questions
On Windows, search Start for Notepad, open it and create a new blank document. Copy the original inputs, the four feasible rows, the two-B conclusion and the failed ratio-first comparison. Press Ctrl+S, select Documents, enter product-mix-V1.txt and choose Save. Close the editor; open Documents in File Explorer and double-click the named file.
Fictional V1: A8−5=3, resource4; B6−4=2, resource3 Demand cap3 each; capacity6; integer units; zero allowed All feasible: (0,0), (0,1), (0,2), (1,0) Best: (0,2); used6; unused0; contribution4 A-first ratio shortcut: (1,0), contribution3 Fixed costs unchanged; contribution is not net profit Missing real evidence and responsible owner: [complete]
Reopening should preserve the integer rule, demand ceilings and zero-production choice. Missing price, variable cost, capacity, usage or demand evidence leaves a real decision unresolved; do not substitute zero. Cash timing is another question, addressed separately by the cash flow guide.
A short practice can produce the original four-row comparison and a saved reason. Completing every sensitivity scenario within fifteen minutes is not a measured participant result. In his public Azerbaijani reflection on perfection and effectiveness, Anar describes projects delayed by pursuing perfection. The application here is finishing one inspectable decision before expanding the model, not claiming he tested this product mix or achieved an earnings result.
Frequently asked questions
Is contribution the same as net profit?
No. This model subtracts the supplied variable cost from price. Fixed expenses and other excluded amounts have not been deducted, so the result is not net profit.
Does the highest resource ratio always win?
Not in this whole-unit example. At capacity six, choosing A first yields contribution three, while two B yield four. Check the complete feasible set.
Which mix wins at capacity nine?
Both zero A with three B and two A with zero B yield contribution six. They use nine and eight resource units respectively.
Can I enter demand three when real demand is unknown?
No. Three is a supplied practice ceiling, not a forecast. Keep a real decision unresolved and identify who can provide the missing evidence.
