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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.
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.
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.
What is the theoretical limit on the number of constraints on a linear programming problem?
There is no limit.
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.
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.
Can a linear programming problem have exactly two optimal solutions?
Yes, a linear programming problem can have exactly two optimal solutions. This will be the case as long as only two decision variables are used within the problem.
How can zero one equations be used to solve mathematical problems efficiently?
Zero-one equations can be used to solve mathematical problems efficiently by representing decision variables as binary values (0 or 1), simplifying the problem into a series of logical constraints that can be easily solved using algorithms like linear programming or integer programming. This approach helps streamline the problem-solving process and find optimal solutions quickly.
What is the minimum number of constraints a linear programming problem can have?
One. To be a (non-trivial) linear programming problem both the objective function and the constraints must be linear. If there were no constraints then the objective function could be made arbitrarily large or arbitrarily small. (Think of a line in two-space.) By adding one constraint the objective function's value can be limited to a finite value.
What is The first step in formulating a linear programming problem?
identifying any upper or lower bounds on the decision variables
How is a problem usually posed in a form?
A problem is typically posed in a form by defining the objective, constraints, and variables involved. This helps to structure the problem and guide the search for a solution using mathematical or computational techniques.
What are the advantages of using Simplex method over graphical method in linear programing?
graphical method is applicable only for solving an LPP having two variables in its constraints , but if more than two variables are used, then it is not possible to use graphical method. In those cases, simplex method helps to solve such problem. In simple, in graphical method is used when the constraints contain two variables only. But simplex method can be used to solve constraints having more than two variables.
