This tool helps you determine the feasible region for a set of linear inequalities.

## How to Use the Feasible Region Calculator

To use the feasible region calculator, follow these steps:

- Enter your constraints in the text area provided. Each constraint should be on a new line, for example:

`x + y ≤ 10`

`x - y ≥ 3`

- Enter your objective function in the input field provided. It should be in the format:

`Maximize z = x + 2y`

or

`Minimize z = 3x - y`

- Click the “Calculate” button to compute the feasible region and obtain the result.

## Output and Limitations

The calculator will display the result in the “Result” field after computing the feasible region based on the given constraints and objective function.

### Limitations

- The current calculator implementation provides a basic feasibility check and should be enhanced for more complex constraint solving.
- Since this implementation does not integrate a sophisticated solver algorithm, the results are only indicative.
- Make sure your constraints and objective functions are formatted correctly as per the examples provided to avoid errors.

## Use Cases for This Calculator

### Calculating Feasible Region for Linear Inequalities

Enter the coefficients and constants of the linear inequalities to visualize and calculate the feasible region where all inequalities are satisfied simultaneously. The calculator will plot the region on a graph and provide the corresponding coordinates.

### Determining Feasible Solutions for Optimization Problems

Input the objective function along with the linear constraints to find the feasible solutions that optimize the objective within the given constraints. Explore the feasible region to identify the maximum or minimum points for the objective.

### Plotting Multiple Inequalities on a Graph

Add multiple linear inequalities to the calculator and see them graphed on the same coordinate plane. Visualizing the intersections and boundaries of the inequalities helps in understanding the feasible region better.

### Checking Infeasible Regions

If the linear inequalities lead to an empty feasible region due to contradictory constraints, the calculator will notify you that there are no feasible solutions. Adjust the inequalities to explore valid regions for your problem.

### Solving Systems of Linear Inequalities

Incorporate systems of linear inequalities into the calculator to determine the regions where all inequalities are satisfied simultaneously. Easily identify the feasible area by analyzing the shaded region on the graph.

### Exploring Corner Points of a Feasible Region

Analyze the corner points of the feasible region to determine the optimal solutions for your problem. By examining the vertices of the region, you can find the points that maximize or minimize the objective function within the constraints.

### Understanding Shadow Prices in Linear Programming

Discover the shadow prices associated with each constraint in your linear programming model by using the feasible region calculator. Shadow prices provide insights into the marginal value of relaxing or tightening the constraints.

### Visualizing Feasible Regions in Two Dimensions

Input the linear inequalities in two dimensions to visualize the feasible regions with ease. The graph representation helps in grasping the feasible region’s shape and boundaries intuitively.

### Iteratively Refining Constraints for Better Solutions

Experiment with different sets of linear inequalities by iteratively refining the constraints and observing the changes in the feasible region. This process allows you to fine-tune the constraints for optimal solutions to your optimization problems.

### Exporting Feasible Region Data for Further Analysis

Export the data related to the feasible region, including coordinates of corner points and shadow prices, for further analysis outside the calculator. This feature enables you to integrate the calculated results into your reports or decision-making processes seamlessly.