Can a linear program have more than one optimal solution?

The multiple optimal solutions will arise in a linear program with more than one set of basic solutions that can minimize or maximize the required objective function. The linear problem can be solved by using the software like MS Excel, but it only provides one optimal solution among many optimal solutions.

Can there be two optimal solutions?

4. If there is more than one optimal solution, then there are uncountably many optimal solutions. 5. If there are several optimal solutions, then there exist at least two basic feasible solutions that are optimal.

How many optimal solutions does a linear programming problem have?

Now, both [ x y ] = [ 1 2 0 ] and [ x y ] = [ 0 1 2 ] are feasible solutions having objective function value . Hence, they are both optimal solutions. (In fact, this problem has infinitely many optimal solutions.

Under what condition is it possible for an LPP to have multiple optimal solutions?

In other words, if at least one of the non-basic variable in the (C i – Z j) row of the final simplex table has a zero value, it indicates that there is more than one optimal solution.

What is the difference between optimal solution and feasible solution?

A feasible solution satisfies all the problem’s constraints. An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). A graphical solution method can be used to solve a linear program with two variables.

What is alternative optimal solution?

An alternate optimal solution is also called as an alternate optima, which is when a linear / integer programming problem has more than one optimal solution. The optimal solution set is a smaller set within the feasible region. Here, the objective function is parallel to cd line segment.

How do you determine an optimal solution?

If there is a solution y to the system AT y = cB such that AT y ≤ c, then x is optimal. By = cB and AT y ≤ c. m i=1 aijyi = ci. are obeyed, then x and y must be optimal.

Can there be infinite optimal solutions?

Optimal solutions exist: Infinitely many! Important Point: This LP is NOT unbounded.

Does an alternative optimal solution exists?

In the presence of degeneracy, the meaning of alternative optimal solutions may not necessarily imply the existence of alternative solution points. These nonbasic variables may then enter the basis (without altering the value of the objective function) and an alternative optimal solution is obtained.

What is feasible solution in LPP?

Definition: A feasible solution to a linear program is a solution that satisfies all constraints. Definition: An optimal solution to a linear program is the feasible solution with the largest objective function value (for a maximization problem).

Is it possible that a linear programming problem has infinite solutions?

An unbounded solution of a linear programming problem is a situation where objective function is infinite. A linear programming problem is said to have unbounded solution if its solution can be made infinitely large without violating any of its constraints in the problem.

Is it possible for a linear programming problem to have no solution?

A linear program is infeasible if there exists no solution that satisfies all of the constraints — in other words, if no feasible solution can be constructed. Since any real operation that you are modelling must remain within the constraints of reality, infeasibility most often indicates an error of some kind.

Where will one find the solution to a LP if a solution exists?

If a solution exists to a bounded linear programming problem, then it occurs at one of the corner points. If a feasible region is unbounded, then a maximum value for the objective function does not exist.

Does every LPP has a solution?

Every LPP admits an optimal solution.

How do you find the number of optimal solution in linear programming?

The values of x and y are said to be optimal solutions for which the objective function z = ax + by is minimum or maximum based on the given linear programming problem.

What is slack variable in simplex method?

Slack variables are additional variables that are introduced into the linear constraints of a linear program to transform them from inequality constraints to equality constraints. If the model is in standard form, the slack variables will always have a +1 coefficient.

How do you find all basic feasible solutions?

A solution in P = {x : Ax ≤ b} is called basic feasible if it has n linearly independent active constraints. Definition 3. A solution in P = {x : Ax ≤ b} is called degenerate if it has more than n linearly independent active constraints.

Can basic feasible solution negative?

In a Basic Solution, the n – m variables at zero are called non- basic variables, while the remaining m variables are called basic variables. If all of the basic variables take non negative values, then the Basic Solution is called a Basic Feasible Solution (BFS).