Linear Programming Calculator
This tool helps you solve optimization problems using linear programming. It is aimed at business operations professionals seeking to optimize resources and costs.
Results
Data Source and Methodology
All calculations are based on standard linear programming formulas and methodologies. For in-depth understanding, refer to "Linear Programming and Network Flows" by Mokhtar S. Bazaraa.
The Formula Explained
Maximize or Minimize: \( z = c_1x_1 + c_2x_2 + \dots + c_nx_n \)
Subject to: \(\sum a_{ij}x_j \leq b_i\), where \(i = 1, 2, \dots, m\) and \(j = 1, 2, \dots, n\)
Glossary of Terms
- Objective Function: The function to be maximized or minimized.
- Constraints: Conditions that the solution must satisfy.
- Optimal Solution: The best possible values for the variables that maximize or minimize the objective function.
- Objective Value: The value of the objective function at the optimal solution.
How It Works: A Step-by-Step Example
Consider the objective function \( z = 3x + 4y \) with constraints \( x + y \leq 10 \) and \( x, y \geq 0 \). The optimal solution is found using simplex or graphical methods.
Frequently Asked Questions (FAQ)
What is Linear Programming?
Linear programming is a mathematical technique for finding the best outcome in a mathematical model whose requirements are represented by linear relationships.
What are the applications of Linear Programming?
It is used in various fields such as economics, business, engineering, and military applications for resource optimization.
How accurate are the results?
The results are accurate as per the input provided and the standard formulations of linear programming.
Can this solver handle non-linear constraints?
No, this tool is designed for linear constraints only.
How do I input constraints?
Each constraint should be entered on a new line, using standard mathematical symbols.