[PDF] a feasible solution to an lp problem

Definition: A feasible solution to a linear program is a solution that satisfies all constraints. Definition: The feasible region in a linear program is the set of all possible feasible solutions.
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  • How to find a feasible solution to the linear programming problem?

    We need to introduce artificial variables to help get an initial feasible solution. We also negate the objective function and convert to a maximization problem. Now all the coefficients in the objective row are negative, so we have an optimal solution. Also, a1 and a2 are both non-basic, so the problem is feasible.

  • Is the feasible solution of an LP is the best solution possible?

    An optimal solution to an LP is a feasible solution such that there does not exist any other feasible solution yielding a better (smaller or larger in the case of minimization and maximization, respectively) objective function value.

  • What is meant by basic feasible solution and optimal solution to a LP problem?

    In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a corner of the polyhedron of feasible solutions. If there exists an optimal solution, then there exists an optimal BFS.
  • Explanation: A feasible solution in linear programming is: A set of values for the decision variables in the problem. Satisfies all the constraints in the problem.
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