Calculator Inputs
Use the responsive form below. It shows three columns on large screens, two on medium screens, and one on small screens.
Example Data Table
| Variable | Objective Coefficient | Type | Lower Bound | Upper Bound |
|---|---|---|---|---|
| x1 | 9 | Integer | 0 | 10 |
| x2 | 5 | Binary | 0 | 1 |
| x3 | 7 | Continuous | 0 | 8 |
| Constraint | x1 | x2 | x3 | Operator | RHS |
|---|---|---|---|---|---|
| C1 | 2 | 4 | 1.5 | ≤ | 14 |
| C2 | 1 | 0 | 1 | ≤ | 8 |
| C3 | 3 | 2 | 2 | ≤ | 20 |
Formula Used
Objective function: Z = c1x1 + c2x2 + c3x3
Constraint form: a1x1 + a2x2 + a3x3 ≤, ≥, or = b
Variable domains: Continuous variables use real values, integer variables use whole numbers, and binary variables use only 0 or 1.
Displayed objective contribution: Contribution of xi = ci × xi
Slack for ≤ constraints: Slack = RHS − LHS
Surplus for ≥ constraints: Surplus = LHS − RHS
Equality residual: Residual = |LHS − RHS|
This page evaluates bounded candidates directly. Continuous variables are searched on the selected step size, so those results are discretized approximations.
How to Use This Calculator
- Choose whether you want to maximize or minimize the objective.
- Enter names, coefficients, types, and bounds for the three decision variables.
- Set a continuous step size. Smaller steps improve detail but increase work.
- Enable up to four constraints and enter each linear expression, operator, and right side value.
- Press Solve Model to generate the result block above the form.
- Review variable values, objective contribution, constraint slack, and the Plotly chart.
- Use the export buttons to save the solved output as CSV or PDF.
FAQs
1. What does this solver calculate?
It evaluates a bounded mixed integer optimization model with three variables and four optional linear constraints. It returns the best feasible objective found within the defined search space.
2. Can I mix variable types?
Yes. Each variable can be continuous, integer, or binary. That lets you model fixed yes or no decisions, count-based choices, and flexible real-valued allocations together.
3. Is the result always exact?
Integer and binary portions are evaluated exactly within their bounds. Continuous variables are searched using your selected step size, so continuous results are discretized approximations.
4. Why does step size matter?
Step size controls how many continuous candidate values are tested. Smaller steps improve precision, but they can greatly increase the number of combinations and processing time.
5. What is slack or residual?
Slack shows unused capacity for less-than constraints. Surplus shows excess over minimum requirements. Equality residual shows how closely the final solution matches the required equality.
6. Why might no feasible solution appear?
Your bounds and constraints may conflict. Review coefficients, operators, right-side values, and variable domains. Even one restrictive condition can remove every possible feasible combination.
7. What should I do if the search space is too large?
Tighten variable bounds, disable unnecessary constraints, or increase the continuous step size. Those changes reduce the number of tested combinations and make solving manageable.
8. What do the CSV and PDF exports include?
They include the solution status, objective value, variable table, and constraint evaluation. This makes it easier to archive, share, or compare scenarios outside the page.