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To solve a linear programming problem with thousands of variables and constraints?
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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 an expression in math?
a collection of symbols that jointly express a quantity
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 the theoretical limit on the number of constraints on a linear programming problem?
There is no limit.
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.
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.
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 is The first step in formulating a linear programming problem?
identifying any upper or lower bounds on the decision variables
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.
What is optimisiom's sturcture?
Optimization is a process of maximizing or minimizing a function by finding its best output. It involves defining a problem, setting objectives and constraints, choosing decision variables, formulating an objective function, and then solving the problem using various optimization techniques like linear programming, gradient descent, or genetic algorithms. The structure of optimization depends on the specific problem being addressed and the approach taken to find the optimal solution.
What is the relation between problem and programming?
Problem -> Programming Programming can be a solution to a problem. If you have a problem and it can be solved by a computer program, so you can create such a program - so you can solve this problem by programming.
What do you understand by linear programming problem?
1. What do you understand by Linear Programming Problem? What are the requirements of Linear Programming Problem? What are the basic assumptions of Linear Programming Problem?
What is the significance of duality theory of linear programming?
fully understanding the shadow-price interpretation of the optimal simplex multipliers can prove very useful in understanding the implications of a particular linear-programming model.It is often possible to solve the related linear program with the shadow prices as the variables in place of, or in conjunctionwith, the original linear program, thereby taking advantage of some computational efficiencies.Understanding the dual problem leads to specialized algorithms for some important classes of linear programming problems. Examples include the transportation simplex method, the Hungarian algorithm for the assignment problem, and the network simplex method. Even column generation relies partly on duality.The dual can be helpful for sensitivity analysis.Changing the primal's right-hand side constraint vector or adding a new constraint to it can make the original primal optimal solution infeasible. However, this only changes the objective function or adds a new variable to the dual, respectively, so the original dual optimal solution is still feasible (and is usually not far from the new dual optimal solution).Sometimes finding an initial feasible solution to the dual is much easier than finding one for the primal. For example, if the primal is a minimization problem, the constraints are often of the form , , for . The dual constraints would then likely be of the form , , for . The origin is feasible for the latter problem but not for the former.The dual variables give the shadow prices for the primal constraints. Suppose you have a profit maximization problem with a resource constraint . Then the value of the corresponding dual variable in the optimal solution tells you that you get an increase of in the maximum profit for each unit increase in the amount of resource (absent degeneracy and for small increases in resource ).Sometimes the dual is just easier to solve. Aseem Dua mentions this: A problem with many constraints and few variables can be converted into one with few constraints and many variables.
