1. What is Linear Programming?

Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. It's widely used in business and economics to solve optimization problems.

2. How Does the Calculator Work?

The calculator solves standard form linear programming problems:

Where:

• \( c \) — Coefficient vector of the objective function
• \( x \) — Vector of variables to be determined
• \( A \) — Matrix of constraint coefficients
• \( b \) — Vector of constraint values

Explanation: The calculator finds values for x that maximize the objective function while satisfying all constraints.

3. Importance of Linear Programming

Details: Linear programming is crucial for resource allocation, production planning, transportation scheduling, and many other optimization problems in various industries.

4. Using the Calculator

Tips: Enter the objective coefficients as comma-separated values. For the constraint matrix, separate rows with semicolons and values within rows with commas. Enter constraint values as comma-separated numbers.

5. Frequently Asked Questions (FAQ)

Q1: What types of problems can this solve?
A: Any standard linear programming problem with linear objective function and constraints.

Q2: What algorithm does this use?
A: The calculator would typically use the Simplex method or an interior-point method.

Q3: Are there size limitations?
A: Very large problems might require specialized software, but this handles typical textbook-sized problems.

Q4: Can it handle equality constraints?
A: The current form handles inequality constraints. Equality constraints would need to be converted to two inequalities.

Q5: What about integer programming?
A: This solves continuous problems. Integer programming requires different techniques.