Can there be 2 optimal solutions?

Can there be 2 optimal solutions?

Hence, when a linear programming problem exhibits multiple optimal solutions (whether pri- mal or dual), it means that the problem at hand is potentially more relevant than a similar problem that exhibits unique optimal solutions.

Can a linear program have more than one optimal solution?

What this means is you can move along that top constraint from one corner to the other without changing the value of your objective function. There are infinitely many optimal solutions which solve the equation: 2×1 + 3×2 == 100/3, between x1==0, and x1==20/3.

Can a linear programming problem have multiple solutions?

Multiple solutions of a linear programming problem are solutions each of which maximize or minimize the objective function under Simplex Method.

How many solutions does a linear program have?

If a linear program has more than one solution, it has infinitely many, as all convex combinations will be solutions.

Can there be infinite optimal solutions?

(l) If H is an optimal solution, there are infinitely many optimal solutions and the limit of the objective function values is plus or minus infinity.

How many optimal solution LPP has?

(C) A LPP can have exactly two different optimal solutions.

What is the optimal solution to a linear programming problem?

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

How might the optimal solution of a linear programming problem be determined?

The values of the decision variables must satisfy a set of constraints, each of which must be a linear inequality or linear equality. 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 find the optimal solution in linear programming?

We determine the optimal solution to the LP by plotting (180x + 160y) = K (K constant) for varying K values (iso-profit lines). One such line (180x + 160y = 180) is shown dotted on the diagram.

Can a linear programming problem have infinite optimal solutions?

A linear programming problem may have i) a unique, finite solution, ii) an unbounded solution iii) multiple (or infinite) number of optimal solutions, iv) infeasible solution and v) a unique feasible point.

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

The multiple optimal solutions are called the alternate basic solution. Alternate or multiple optimal solutions occurs in LLP problem when the objective function line is parallel to one of the binding constraint lines or objective function line and constraint line have the same slope.

Can basic optimal solutions be infinite?

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

How many solutions does the linear programming problem have?

Given that an optimal solution to a linear programming problem exists, it must occur at a vertex of the feasible set. If the optimal solution occurs at two adjacent vertices of the feasible set, then the linear programming problem has infinitely many solutions. Any point on the line segment joining the two vertices is also a solution.

How do you solve linear programming problems with bounded sets?

A linear programming problem with a bounded set always has an optimal solution. This means that a bounded set has a maximum value as well as a minimum value. Example 1: Given the objective function P x y= −10 3 and the following feasible set, A. Find the maximum value and the point where the maximum occurs.

What is a feasible set in linear programming problems?

Recall that the solution set to a system of inequalities is the region that satisfies all inequalities in the system. In linear programming problems, this region is called the feasible set, and it represents all possible solutions to the problem.

How to solve linear programming problems in R?

If you’re using R, solving linear programming problems becomes much simpler. That’s because R has the lpsolve package which comes with various functions specifically designed for solving such problems.