Can you have exactly 2 optimal solutions?

Answer. “No, it is not possible for an LP model to have exactly two optimal solutions.” A LP model may have either 1 optimal solution or more than 1 optimal solution, but it cannot have exactly 2 optimal solutions.

Can a linear programming problem have multiple optimal solutions?

A feasible point on the optimal objective function line is an optimal solution. A linear programming problem can have multiple optimal solutions. If a single optimal solution exists while using the graphical method to solve a linear programming problem, it will exist at a corner point.

How many optimal solutions can a linear programming problem have?

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 program have exactly two basic feasible solutions?

Let’s say our objective function is of the form ax+by=c,where a>0,b>0 and c is the value we wish to maximize. The maximum value of our ‘c’ will be achieved only at these two points and nowhere else. Hence, we can have exactly two optimal solutions.

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.

When can alternative multiple optimal solutions occur in a LP model?

When do alternate optimal solutions occur in LP models? When a constraint is parallel (overlapped) to a level curve.

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.

Can there be multiple optimal solutions to an assignment problem how do you identify such situations?

Sometimes, it is possible to cross out all the zeros in the reduced matrix in two or more ways. If you can choose a zero cell arbitrarily, then there will be multiple optimal solutions with the same total pay-off for assignments made.

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 an optimal solution be unbounded?

Learn that an unbounded Optimal solution means having a closed unbounded feasible region, however, the inverse of this statement may not be correct. An unbound optimal solution means the constraints do not limit the optimal solution and the feasible region effectively extends to infinity.

Can an unbounded linear program have an optimal solution?

If a linear program is feasible but not (objective) unbounded, then it must achieve a finite optimal value within its feasibility set; in other words, it has an optimal solution x∗ ∈S⊂F.

Under what condition is it possible for an LPP to have more than one optimal solution What do these optimal solutions represent?

The necessary condition for the existence of LP multiple solutions: If the total number of zeros in the Reduced Cost together with number of zeros in the Shadow Price columns exceeds the number of constraints, then you might have multiple solutions.