What is the difference between a feasible solution a basic feasible solution and an optimal solution of a linear programming problem?

In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. If there exists an optimal solution, then there exists an optimal BFS. Hence, to find an optimal solution, it is sufficient to consider the BFS-s.

What is difference between feasible solution and basic feasible solution?

Decision Vector: A vector of some or all (usually all) of the decision variables in a mathematical program. Degenerate basic feasible solution: A basic feasible solution where one or more of the basic variables is zero. Feasible Solution: A solution that satisfies all the constraints.

What is the difference between initial basic feasible solution and optimal solution?

A set of non-negative allocations xij ≥ 0 which satisfies the row and column restrictions is known as feasible solution. A feasible solution (not necessarily basic) is said to be optimal if it minimizes the total transportation cost. There are three different methods to obtain the initial basic feasible solution.

What is the meaning of basic solution?

A basic solution is an aqueous solution containing more OH-ions than H+ions. In other words, it is an aqueous solution with a pH greater than 7. Basic solutions contain ions, conduct electricity, turn red litmus paper blue, and feel slippery to the touch.

What is meant by basic solution?

What is feasible and basic feasible solution?

A feasible solution is a set of values for the decision variable that satisfies all the constraints in an optimisation problem. BASIC FEASIBLE SOLUTION. A basic solution that satisfies all the constraints defining or in other words one that lies with in is called basic feasible solution.

Are basic solutions extreme points?

The basic variables must include x1 and x4. If we choose x2 as a basic variable, then the resulting system has linearly independent columns. Thus, the solution is a basic feasible solution, i.e., an extreme point.

Is it true that P has at least one basic feasible solution?

By definition, a basic feasible solution (BFS from now on) must satisfy both Ax=b and x≥0. Therefore, if P=∅, P has no BFS. However, by weakening the hypothesis one can show that P will always have at a least one BFS.

How do you identify a basic feasible solution?

A solution in P = {x : Ax ≤ b} is called basic feasible if it has n linearly independent active constraints. Definition 3. A solution in P = {x : Ax ≤ b} is called degenerate if it has more than n linearly independent active constraints.

What do you mean by feasible solution?

A feasible solution is a set of values for the decision variables that satisfies all of the constraints in an optimization problem. The set of all feasible solutions defines the feasible region of the problem.