Quick Answer: What Is A Optimal Solution?

Is the optimal solution unique?

(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.

Suppose that x, a feasible solution, is unique optimal.

Then this means that for any y E P such that y + x, then c’x < c'y.

Let d be any nonzero feasible direct at x..

What is the difference between feasible solution and optimal solution?

A solution (set of values for the decision variables) for which all of the constraints in the Solver model are satisfied is called a feasible solution. … An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost.

What is meant by feasible solution?

A feasible solution is a set of values for the decision variables that satisfies all of the constraints in an optimization problem. The set of all feasible solutions defines the feasible region of the problem.

What is unique optimal solution?

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.

Why is simplex method used?

The simplex method is used to eradicate the issues in linear programming. It examines the feasible set’s adjacent vertices in sequence to ensure that, at every new vertex, the objective function increases or is unaffected. … Furthermore, the simplex method is able to evaluate whether no solution actually exists.

What is the optimal solution in linear programming?

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).

Why can’t solver find a feasible solution?

This message appears when Solver could not find any combination of values for the decision variables that allows all of the constraints to be satisfied simultaneously. If you are using the Simplex LP Solving method, and the model is well scaled, Solver has determined for certain that there is no feasible solution.

How can we solve the transportation problem?

Algorithm for Least Cost Method (LCM)Select the smallest transportation cost cell available in the entire table and allocate the supply and demand.Delete that row/column which has exhausted. … Again select the smallest cost cell in the existing table and allocate. ( … Obtain the initial basic feasible solution.

What is optimal solution in simplex method?

The method produces an optimal solution to satisfy the given constraints and produce a maximum zeta value. To use the Simplex method, a given linear programming model needs to be in standard form, where slack variables can then be introduced. Using the tableau and pivot variables, an optimal solution can be reached.

What is optimal solution in transportation problem?

Optimal Solution- a feasible solution is said to be optimal solution if it minimize total transportation cost Balanced Transportation Problem – a transportation problem in which the total supply from all sources is equal to the total demand in all the destinations.