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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.
Can a linear programming problem have two optimal solutions?
No. However, a special subset of such problems: integer programming, can have two optimal solutions.
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 are dependent and independent variables and how are they usually related to each other in a problem or situation?
a DEPENDENT variable is one of the two variables in a relationship.its value depends on the other variable witch is called the independent variable.the INDEPENDENT variable is one of the two variables in a relationship . its value determines the value of the other variable called the independent variable.
The answer to a multiplication problem is called a?
When two variables are multiplied, the result is called a product. When they are divided, it is a quotient. Addition results in a sum and subtraction results in a difference.
What is non linear programming problem?
It is a programming problem in which the objective function is to be optimised subject to a set of constraints. At least one of the constraints or the objective functions must be non-linear in at least one of the variables.
In linear programming what are limits on the values of the variables called?
In linear programming, limits on the values of the variables are called "constraints." These constraints define the feasible region within which the solution to the optimization problem must lie. They can take the form of inequalities or equalities, restricting the values that the decision variables can assume. Constraints are essential in ensuring that the solution meets specific requirements or conditions of the problem.
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 are the rules for converting a primal problem into its dual?
To convert a primal linear programming problem into its dual, the following rules apply: If the primal is a maximization problem with constraints in the form of inequalities (≤), the dual will be a minimization problem with constraints in the form of inequalities (≥). The coefficients of the objective function in the primal become the right-hand side constants in the dual, while the right-hand side constants of the primal become the coefficients in the dual's objective function. The primal's variables correspond to the dual's constraints and vice versa, effectively switching their roles. Additionally, if the primal has ( m ) constraints and ( n ) variables, the dual will have ( n ) constraints and ( m ) variables.
How we convert the primal into dual problem in lpp?
To convert a primal linear programming problem into its dual, we first identify the primal's objective function and constraints. If the primal is a maximization problem with ( m ) constraints and ( n ) decision variables, the dual will be a minimization problem with ( n ) constraints and ( m ) decision variables. The coefficients of the primal objective function become the right-hand side constants in the dual constraints, while the right-hand side constants of the primal constraints become the coefficients in the dual objective function. Additionally, the direction of inequalities is reversed: if the primal constraints are ( \leq ), the dual will have ( \geq ) constraints, and vice versa.
When does infeasibility occur in a linear programming problem?
Infeasibility occurs in a linear programming problem when there is no solution that satisfies all the constraints simultaneously.
How can the reduction of vertex cover to integer programming be achieved?
The reduction of vertex cover to integer programming can be achieved by representing the vertex cover problem as a set of constraints in an integer programming formulation. This involves defining variables to represent the presence or absence of vertices in the cover, and setting up constraints to ensure that every edge in the graph is covered by at least one vertex. By formulating the vertex cover problem in this way, it can be solved using integer programming techniques.
What is the theoretical limit on the number of constraints on a linear programming problem?
There is no limit.
What are the four representations in a linear problem?
In a linear programming problem, the four main representations are: Objective Function: This defines the goal of the optimization, typically to maximize or minimize a certain quantity. Constraints: These are the limitations or restrictions placed on the variables, expressed as linear inequalities or equations. Decision Variables: These are the variables that decision-makers will choose values for in order to achieve the best outcome. Feasible Region: This is the set of all possible points that satisfy the constraints, representing all feasible solutions to the problem.
What is a structural variable in linear programming?
A structural variable in linear programming refers to a variable that directly influences the constraints and objectives of the model. These variables typically represent decision variables that determine the allocation of resources, such as quantities of products to produce or resources to allocate. They are essential for defining the feasible region of the optimization problem and play a crucial role in achieving the desired outcome in the linear programming formulation.
How do I figure out the programming decision and variables for anything?
There is no programming solution for "anything". Programs are specifically designed to solve a particular problem.
What are the decision variables?
Decision variables are the variables that decision-makers can control or manipulate in an optimization problem or mathematical model. They represent the choices available to the decision-maker, and their values are determined through the optimization process to achieve the best possible outcome, such as maximizing profit or minimizing cost. In a linear programming context, these variables are often subject to certain constraints that limit their feasible values.
