Feasible solutions and basic feasible solutions are two important concepts in linear programming, which is a mathematical method used to optimize the allocation of limited resources in order to achieve a specific objective. While both types of solutions involve finding the optimal values for the variables in a given linear programming problem, they differ in the constraints that they satisfy.

A feasible solution is any set of values for the variables in a linear programming problem that satisfies all of the constraints of the problem. In other words, it is a solution that is possible to achieve given the constraints of the problem. Feasible solutions may not necessarily be optimal, as they may not yield the highest or lowest possible value for the objective function.

On the other hand, a basic feasible solution is a special type of feasible solution in which a subset of the variables in the problem are set to zero, while the remaining variables are set to non-zero values. These non-zero variables are known as basic variables, and the subset of constraints that they satisfy are known as the basic feasible solutions.

Basic feasible solutions have a number of important properties that make them useful in linear programming. One of the most important properties of basic feasible solutions is that they form a basis for the feasible region of the problem, which is the set of all possible feasible solutions. This means that any feasible solution can be represented as a linear combination of basic feasible solutions.

In addition, basic feasible solutions are often easier to find than other feasible solutions, as they involve setting only a subset of the variables to non-zero values. This can make it faster and more efficient to solve linear programming problems using basic feasible solutions.

In summary, feasible solutions are any set of values for the variables in a linear programming problem that satisfies all of the constraints, while basic feasible solutions are a special type of feasible solution in which a subset of the variables are set to zero and the remaining variables are set to non-zero values. Both types of solutions are important in linear programming, but basic feasible solutions have additional properties that make them particularly useful in finding optimal solutions to linear programming problems.

## What is an infeasible solution?

By optimum point or points , I mean the point on the curve in which the increase of the value in X axis by 1 point, does not yield neither a very high nor a very low increase in the value of Y e. We say that a linear programming problem is degenerate if it contains degenerate vertices or basic feasible solutions. No further increase in profit is possible. If there are several optimal solutions, then there exist at least two basic feasible solutions that are optimal. For example, in an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a decision variable. Bill tells Jocelyn that the minimum cost method, sometimes called the minimum cell cost method or least cost method, is used when the priority is to reduce costs for distribution of materials. Apr 2005 Basic feasible solution means the 1 st simplex table.