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What is the feasible region of a linear programming problem?
After graphing the equations for the linear programming problem, the graph will have some intersecting lines forming some polygon. This polygon (triangle, rectangle, parallelogram, quadrilateral, etc) is the feasible region.
What is infeasibility in linear programming?
In linear programming, infeasibility refers to a situation where no feasible solution exists for a given set of constraints and objective function. This can occur when the constraints are contradictory or when the feasible region is empty. Infeasibility can be detected by solving the linear programming problem and finding that no solution satisfies all the constraints simultaneously. In such cases, the linear programming problem is said to be infeasible.
What is the difference between linear and integer programming?
Integer programming is a method of mathematical programming that restricts some or all of the variables to integers. A subset of Integer programming is Linear programming. This is a form of mathematical programming which seeks to find the best outcome in such a way that the requirements are linear relationships.
What is the minimum value of 6x plus 5y in the feasible region excluding point (0 0)?
The answer depends on the feasible region and there is no information on which to determine that.
Who invented linear programming?
George B. Dantzig
Is it possible for a linear programming problem to have no solution?
Yes. There need not be a feasible region.
What is the feasible region of a linear programming problem?
After graphing the equations for the linear programming problem, the graph will have some intersecting lines forming some polygon. This polygon (triangle, rectangle, parallelogram, quadrilateral, etc) is the feasible region.
What is optimal feasible solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
Distinguish between integer programming problem and linear programming problem?
Integer programming is a subset of linear programming where the feasible region is reduced to only the integer values that lie within it.
Can a linear programming problem have multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
How do you solve linear programming with no feasible region?
When a linear programming problem has no feasible region, it typically indicates that the constraints are contradictory, making it impossible to find a solution that satisfies all conditions. To address this, first, review the constraints for inconsistencies or errors. If contradictions are found, reformulate the problem by adjusting constraints to create a feasible region. If adjustments are not possible, it may be necessary to reconsider the problem's formulation or objectives.
Where will the maximum value of a feasible region?
The maximum value of a feasible region, typically in the context of linear programming, occurs at one of the vertices or corner points of the region. This is due to the properties of linear functions, which achieve their extrema at these points rather than within the interior of the feasible region. To find the maximum value, you evaluate the objective function at each vertex and select the highest result.
What is infeasibility in linear programming?
In linear programming, infeasibility refers to a situation where no feasible solution exists for a given set of constraints and objective function. This can occur when the constraints are contradictory or when the feasible region is empty. Infeasibility can be detected by solving the linear programming problem and finding that no solution satisfies all the constraints simultaneously. In such cases, the linear programming problem is said to be infeasible.
What is the strong duality proof for linear programming problems?
The strong duality proof for linear programming problems states that if a linear programming problem has a feasible solution, then its dual problem also has a feasible solution, and the optimal values of both problems are equal. This proof helps to show the relationship between the primal and dual problems in linear programming.
What is simplex method of linear programming?
The simplex method is an algorithm used for solving linear programming problems, which aim to maximize or minimize a linear objective function subject to linear constraints. It operates on a feasible region defined by these constraints, moving along the edges of the feasible polytope to find the optimal vertex. The method iteratively improves the solution by pivoting between basic feasible solutions until no further improvements can be made. It's widely used due to its efficiency and effectiveness in handling large-scale linear optimization problems.
What is the maximum value of 5x 2y in the feasible region?
To find the maximum value of the expression (5x + 2y) in a feasible region, you would typically use methods such as linear programming, considering constraints that define the feasible region. By evaluating the vertices of the feasible region, you can determine the maximum value. Without specific constraints provided, it's impossible to give a numerical answer. Please provide the constraints for a detailed solution.
What is the definition of the solution of linear inequalities?
Each linear equation is a line that divides the coordinate plane into three regions: one "above" the line, one "below" and the line itself. For a linear inequality, the corresponding equality divides the plane into two, with the line itself belonging to one or the other region depending on the nature of the inequality. A system of linear inequalities may define a polygonal region (a simplex) that satisfies ALL the inequalities. This area, if it exists, is called the feasible region and comprises all possible solutions of the linear inequalities. In linear programming, there will be an objective function which will restrict the feasible region to a vertex or an edge of simplex. There may also be a further constraint - integer programming - where the solution must comprise integers. In this case, the feasible region will comprise all the integer grid-ponits with the simplex.
