Question: What Is An Optimal Solution?

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..

How do you add a constraint in Excel?

Excel Solver – Add, change or delete a ConstraintIn the Solver Parameters dialog box, under Subject to the Constraints, click Add.In the Cell Reference box, enter the cell reference or name of the cell range whose value(s) you want to constrain. … Click the relationship ( <=, =, >=, int, bin, or dif ) that you want between the referenced cell(s) and the constraint.More items…

What is optimal basic 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. A globally optimal solution is one where there are no other feasible solutions with better objective function values.

What is an unbounded solution?

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.

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.

How can we solve maximization problem using simplex method?

Set up the problem. … Convert the inequalities into equations. … Construct the initial simplex tableau. … The most negative entry in the bottom row identifies the pivot column.Calculate the quotients. … Perform pivoting to make all other entries in this column zero.More items…•

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).

How do you know if a solution is optimal?

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.

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.

When a model has a unique optimal solution it means that?

Unique optimal solution. When a model has a unique optimal solution, it means that there is exactly one solution. that will result in the maximum (or minimum) objective.

Why does solver not work in Excel?

Sometimes it happens that the ActiveX settings in Office Application are disabled and for that reason, it shows you excel solver add-in not working. To make it work then follow the below-given steps to check ActiveX settings: Open Excel. Click on File>Options>Trust Centre.

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 the optimal solution for knapsack problem?

After selecting item A, no more item will be selected. Hence, for this given set of items total profit is 24. Whereas, the optimal solution can be achieved by selecting items, B and C, where the total profit is 18 + 18 = 36.

Is the optimal solution unique?

primal optimal solution x0 is a sufficient condition for the uniqueness of the dual optimal solution. On the other hand, it is also known that if the primal feasible set is nonempty, but it has no inner point, then there is no unique dual optimal solution.

What is unique optimal solution?

(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.

When would you use simplex LP?

Simplex LP – This is used to solve linear problems. Evolutionary – This is used to solve more complex and non-smooth non-linear problems. It looks for a global optimal solution, which makes it take longer to run compared to GRG Nonlinear.

What is the meaning of optimal?

: most desirable or satisfactory : optimum the optimal use of class time the optimal dosage of medication for a patient conditions for optimal development.

What is slack variable in optimization?

In an optimization problem, a slack variable is a variable that added to an inequality constraint to transform it into an equality. Introducing a slack variable replaces an inequality constraint with an equality constraint and a non-negativity constraint on the slack variable.

Why can’t solver find a feasible solution?

Solver could not find a feasible solution The message tells you that your optimization modeling problem doesn’t have an answer. As a practical matter, when you see this message, it means that your set of constraints excludes any possible answer.

What is the difference between feasible solution and basic feasible solution?

Degenerate basic feasible solution: A basic feasible solution where one or more of the basic variables is zero. … Feasible Solution: A solution that satisfies all the constraints. Feasible Region: The set of all feasible solutions, i.e., S.

How do you do transportation problems?

Solution: Step 1: Check whether the problem is balanced or not. If the total sum of all the supply from sources O1, O2, and O3 is equal to the total sum of all the demands for destinations D1, D2, D3 and D4 then the transportation problem is a balanced transportation problem.