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Explaining the solution to your typical linear programming problem is the main objective of creating this site.
Explaining the solution to your typical linear programming problem is the main objective of creating this site.
Graphical Method of Linear Programming Problem
This method allows solving the linear programming problem for the function of two variables.
This is the first problem that is solved when studying linear programming.
Each step of the solution is illustrated with detailed comments and a neat picture.
Example ¹1. Function has a maximum value at the point
Example ¹2. Function has a minimum value at the point
Example ¹3. Function has a maximum value on the line segment
Example ¹4. Function has a minimum value on the line segment
Example ¹5. Function has a maximum value on the ray
Example ¹6. Function has a minimum value on the ray
Example ¹7. Function increases unlimitedly
Example ¹8. Function decreases unlimitedly
Example ¹9. Region of feasible solutions is a point
Example ¹10. Region of feasible solutions is an empty set
This method allows solving the linear programming problem for the function of two variables.
This is the first problem that is solved when studying linear programming.
Each step of the solution is illustrated with detailed comments and a neat picture.
Example ¹1. Function has a maximum value at the point
Example ¹2. Function has a minimum value at the point
Example ¹3. Function has a maximum value on the line segment
Example ¹4. Function has a minimum value on the line segment
Example ¹5. Function has a maximum value on the ray
Example ¹6. Function has a minimum value on the ray
Example ¹7. Function increases unlimitedly
Example ¹8. Function decreases unlimitedly
Example ¹9. Region of feasible solutions is a point
Example ¹10. Region of feasible solutions is an empty set
Simplex Method
The simplex method is universal. It allows you to solve any linear programming problems.
Òhe solution by the simplex method is not as difficult as it might seem at first glance.
This program finds a general solution only for the case when the solution is a line segment.
Example ¹1. Simplex method. Finding a maximum value of the function
Example ¹2. Simplex method. Finding a minimum value of the function
Example ¹3. Simplex method. Finding a maximum value of the function (artificial variables)
Example ¹4. Simplex method. Finding a minimum value of the function (artificial variables)
Example ¹5. Simplex method. Solution is not the only one
Example ¹6. Simplex method. Function increases unlimitedly
Example ¹7. Simplex method. Function decreases unlimitedly
Example ¹8. Simplex method. Region of feasible solutions is an empty set
The simplex method is universal. It allows you to solve any linear programming problems.
Òhe solution by the simplex method is not as difficult as it might seem at first glance.
This program finds a general solution only for the case when the solution is a line segment.
Example ¹1. Simplex method. Finding a maximum value of the function
Example ¹2. Simplex method. Finding a minimum value of the function
Example ¹3. Simplex method. Finding a maximum value of the function (artificial variables)
Example ¹4. Simplex method. Finding a minimum value of the function (artificial variables)
Example ¹5. Simplex method. Solution is not the only one
Example ¹6. Simplex method. Function increases unlimitedly
Example ¹7. Simplex method. Function decreases unlimitedly
Example ¹8. Simplex method. Region of feasible solutions is an empty set
Transportation Problem of Linear Programming
The transportation problem is a special linear programming problem.
The program finds the initial solution by the North-West corner method or the least cost method.
If necessary, the initial solution is improved by the potential method.
The solution is accompanied by a large number of illustrations.
Example ¹1. Transportation problem by the least cost method (Balanced problem)
Example ¹2. Transportation problem by the least cost method (Unbalanced problem. Fictitious supplier)
Example ¹3. Transportation problem by the least cost method (Unbalanced problem. Fictitious consumer)
Example ¹4. Transportation problem by the North-West corner method (Balanced problem)
Example ¹5. Transportation problem by the North-West corner method (Unbalanced problem. Fictitious supplier)
Example ¹6. Transportation problem by the North-West corner method (Unbalanced problem. Fictitious consumer)
The transportation problem is a special linear programming problem.
The program finds the initial solution by the North-West corner method or the least cost method.
If necessary, the initial solution is improved by the potential method.
The solution is accompanied by a large number of illustrations.
Example ¹1. Transportation problem by the least cost method (Balanced problem)
Example ¹2. Transportation problem by the least cost method (Unbalanced problem. Fictitious supplier)
Example ¹3. Transportation problem by the least cost method (Unbalanced problem. Fictitious consumer)
Example ¹4. Transportation problem by the North-West corner method (Balanced problem)
Example ¹5. Transportation problem by the North-West corner method (Unbalanced problem. Fictitious supplier)
Example ¹6. Transportation problem by the North-West corner method (Unbalanced problem. Fictitious consumer)
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