What is a feasible solution in LPP?
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What is a feasible solution in LPP?
A feasible solution to an LP problem must satisfy all of the problem’s constraints simultaneously. A feasible solution is a set of values for the decision variables that satisfies all of the constraints in an optimization problem.
How do you define a feasible solution?
A feasible solution is one that satisfies all defined constraints and requirements. A solution is infeasible when no combination of decision variable values can satisfy the entire set of requirements and constraints.
What is feasible solution and optimal solution?
A feasible solution satisfies all the problem’s constraints. An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). A graphical solution method can be used to solve a linear program with two variables.
What is feasible region and feasible solution?
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem’s constraints, potentially including inequalities, equalities, and integer constraints.
What is basic feasible solution example?
Example. Consider the following linear program. Say we start with B = {3,4} and N = {1,2}. It should be clear that the resulting solution (x1 = 0,x2 = 0,x3 = 1,x4 = 1) is a basic feasible solution (Verify that the corresponding columns of A are linearly independent).
What is initial feasible solution?
The initial basic feasible solution (IBFS) is a significant step to achieve the minimal total cost (optimal solution) of the transportation problem. However, the existing methods of IBFS do not always provide a good feasible solution which can reduce the number of iterations to find the optimal solution.
What is optimal solution of LPP?
A feasible solution to an LPP with a maximization problem becomes an optimal solution when the objective function value is the largest (maximum). Similarly, a feasible solution to an LPP with a minimization problem becomes an optimal solution when the objective function value is the least (minimum).
What is optimal solution in LPP?
How do you define a feasible region?
A feasible region is an area defined by a set of coordinates that satisfy a system of inequalities. The region satisfies all restrictions imposed by a linear programming scenario.
Which of the following is the definition of the feasible region?
1 Answer. The feasible region is the set of all points whose coordinates satisfy the constraints of a problem.
What is difference between basic solution and basic feasible solution?
(1) A solution x of Ax = b is called a basic solution if the vectors {ai : xi = 0} are linearly independent. (That is, columns of A corresponding to non-zero variables xi are linearly independent.) (2) A basic solution satisfying x ⩾ 0 is called a basic feasible solution (BFS).
What is basic feasible solution in TP?
A feasible solution is said to be basic if the number of positive allocations equals m+n-1; that is one less than the number of rows and columns in a transportation problem.
What is initial basic feasible solution in quantitative methods?
In general, any basic feasible solution of a transportation problem with m origins (such as factories) and n destinations (such as warehouses) should have ‘m + n – 1’ non zero basic variables.
What feasible solution satisfies?
The answer is a feasible solution of a linear program that always satisfies all the constraints because a linear program is an algorithm, which will satisfy the objective function so a feasible solution must satisfy all the constraints of a linear program.
How do you identify a feasible region in LPP?
To solve the given linear programming problem, linear inequalities are drawn on graphs and the inequality (≤,≥) tells us the region, which particular linear inequality will cover. When all linear inequalities are drawn on a graph, the common region for all of them represents a feasible region.
What is feasible region with example?
In an optimisation problem, there are typically a number of constraints on the variables. For example, a problem might be to find the maximum possible value of 2x+3y subject to the constraints x≥0y≥0x+y≤10y≥x−2.
What is meant by feasible region in graphical method?
The feasible solution region on the graph is the one which is satisfied by all the constraints. It could be viewed as the intersection of the valid regions of each constraint line as well. Choosing any point in this area would result in a valid solution for our objective function.
What is the difference between feasible solution and basic feasible solution of LPP?
Degenerate basic feasible solution: A basic feasible solution where one or more of the basic variables is zero. Discrete Variable: A decision variable that can only take integer values. Feasible Solution: A solution that satisfies all the constraints. Feasible Region: The set of all feasible solutions, i.e., S.
What do u mean by feasible region?
The common region determined by all the constraints including non-negative constraints x,y≥0 of a linear programming problem is called the feasible region (or solution region) for the problem. Mathematics.
