How do you find alternative optimal solution in simplex method?

– In Simplex algorithm, alternative solutions are detected when there are 0 valued coefficients for nonbasic variables in row-0 of the optimal tableau. – If there is no nonbasic variable with a zero coefficient in row 0 of the optimal tableau, the LP has a unique optimal solution.

What is optimal solution in programming?

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

What is a unique optimal solution in linear programming?

unique optimal solution. Our method requires the solution of only one extra LPP such that the original problem has. alternative solutions if and only if the optimal value of the new LPP is positive. If the original solution is not unique, an. alternative solution is displayed.

What is optimal value in linear programming?

If a linear programming problem can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions. For example, the maximum or minimum value of f(x,y)=ax+by+c over the set of feasible solutions graphed occurs at point A,B,C,D,E or F .

What is multiple optimal solution in LPP?

Explanation: The multiple optimal solutions arise in a linear programming problem with more than one set of basic solutions that can minimize or maximize the required objective function. The multiple optimal solutions are called the alternate basic solution.

How do you know if an optimal solution is unique?

Since y was an arbitrary point in P, it follows that x is an optimal solution. This proves the equality. (b) A feasible solution x is the unique optimal solution if and only if c’d > 0 for every nonzero feasible direction d at x.

What is optimal value linear programming?

Is the basic optimal solution unique?

By definition, a BFS has at most m non-zero variables and at least n-m zero variables. A BFS can have less than m non-zero variables; in that case, it can have many different bases, all of which contain the indices of its non-zero variables. is non-singular, so the constraint has a unique solution.