Build integer plans from limits and margins. Review feasible mixes across machine, labor, and demand. Use this solver to balance output, profit, and capacity.
| Product | Price | Variable Cost | Demand | Min Units | Max Units | Machine Per Unit | Labor Per Unit | Material Per Unit |
|---|---|---|---|---|---|---|---|---|
| Product A | 90 | 50 | 18 | 0 | 18 | 2 | 3 | 4 |
| Product B | 75 | 40 | 20 | 0 | 20 | 1 | 2 | 3 |
| Product C | 110 | 70 | 16 | 0 | 16 | 3 | 2 | 5 |
Shared capacities: Machine Hours = 48, Labor Hours = 50, Material Units = 70.
Contribution Per Unit = Selling Price Per Unit - Variable Cost Per Unit
Objective = Maximize Z = (c1 × x1) + (c2 × x2) + (c3 × x3)
Machine Constraint = (m1 × x1) + (m2 × x2) + (m3 × x3) ≤ Machine Capacity
Labor Constraint = (l1 × x1) + (l2 × x2) + (l3 × x3) ≤ Labor Capacity
Material Constraint = (r1 × x1) + (r2 × x2) + (r3 × x3) ≤ Material Capacity
Bounds = Minimum Units ≤ xi ≤ min(Demand Limit, Maximum Units)
Integer Rule = x1, x2, and x3 must be whole numbers.
An integer production mix solver helps planners decide how many whole units of each product to make. This matters when output cannot be split into fractions. A workshop can build 7 units or 8 units. It cannot build 7.4 finished items. The calculator turns that real planning issue into a clear optimization task. You enter prices, variable costs, demand limits, and resource usage. The solver then checks feasible integer combinations and returns the best profit plan.
Production planning often depends on limited machine hours, labor hours, and material stock. Each product uses these resources in a different way. A high margin item may consume too much machine time. A fast item may use less labor but more material. This calculator compares those tradeoffs directly. It shows where slack remains and which resource becomes the active bottleneck. That makes capacity planning more practical and easier to explain.
Profit optimization is not only about choosing the product with the highest selling price. It depends on contribution margin and on how efficiently each unit uses scarce resources. This tool calculates contribution for every product and tests combinations against limits. That helps managers avoid guesswork. It also helps teams compare feasible mixes before approving a batch schedule, short run plan, or weekly production target.
The calculator is useful in operations management, industrial engineering, manufacturing math, and classroom optimization exercises. It can support batch planning, product mix analysis, and entry level linear programming lessons. Because the model uses integers, the result matches real production settings more closely. You can also add minimum commitments, maximum unit caps, and demand ceilings to reflect practical business rules.
The result section shows optimal units for each product, total revenue, total variable cost, and best profit. It also shows machine, labor, and material usage with slack values. Slack is important because it reveals unused capacity. The top feasible plans table gives strong alternatives when managers want more than one choice. This makes the page useful for decision support, review meetings, and quick what-if testing.
When demand changes or costs move, you can update inputs and solve again in seconds. That creates a repeatable workflow for production mix analysis. The tool is simple enough for daily use but detailed enough for serious planning. It supports cleaner resource allocation, better profit control, and clearer operational decisions based on whole-unit production rules.
Many production plans require whole units, batches, or jobs. Integer solving avoids fractional outputs that may look valid in math but fail in real operations.
Contribution per unit equals selling price minus variable cost. The calculator uses that value in the objective function to maximize total contribution or profit.
Demand limit reflects sales capacity. Maximum units reflect production policy or technical limits. Using both lets you model market and operational restrictions separately.
Slack is unused capacity. If machine slack is 5, then 5 machine hours remain after the selected plan is produced.
The current limits conflict. Reduce minimum units, increase capacity, lower resource usage, or revise demand and maximum values until a feasible combination appears.
It is a compact three-product integer solver. It is ideal for small planning models, teaching, and quick analysis rather than large industrial optimization projects.
The page caps the search at 200 units per product to keep runtime stable in shared hosting and general browser-based workflows.
Use a larger optimizer when you need many products, many resources, setup times, fixed costs, or advanced constraints such as multi-period planning.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.