## What do you mean by revised simplex method?

The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the constraints adjusted to a set of basic variables, it maintains a representation of a basis of the matrix representing the constraints.

**What is the difference between simplex method and revised simplex method?**

In simplex method the entire simplex tableau is updated while a small part of it is used. The revised simplex method uses exactly the same steps as those in simplex method. The only difference occurs in the details of computing the entering variables and departing variable as explained below.

**Why revised simplex method is preferred is preferred over other methods?**

For such problems the revised simplex method is preferred since it permits the (hyper-)sparsity of the problem to be exploited. This is achieved using techniques for factoring sparse matrices and solving hyper-sparse linear systems. The standard simplex method is also unstable numerically.

### What is the simplex multipliers in the revised simplex method?

The simplex multipliers (y1, y2,…, ym) associated with a particular basic solution are the multiples of their initial system of equations such that, when all of these equations are multiplied by their respective simplex multipliers and subtracted from the initial objective function, the coefficients of the basic …

**What is the advantage of duality?**

Even column generation relies partly on duality. The dual can be helpful for sensitivity analysis. Changing the primal’s right-hand side constraint vector or adding a new constraint to it can make the original primal optimal solution infeasible.

**What is the advantage of revised simplex method over simplex method?**

The inaccuracies due to rounding errors in the original simplex method are avoided in the revised simplex method if the basis matrix is reinverted at regular periods. The revised simplex method allows special routines for sparse matrix manipulations to be exploited when the original constraint matrix is sparse.

#### What are the advantages of revised simplex method over regular simplex method?

**Why duality is used in linear programming?**

In linear programming, duality implies that each linear programming problem can be analyzed in two different ways but would have equivalent solutions. Any LP problem (either maximization and minimization) can be stated in another equivalent form based on the same data.

**What is difference between primal and dual?**

In the primal problem, the objective function is a linear combination of n variables. In the dual problem, the objective function is a linear combination of the m values that are the limits in the m constraints from the primal problem.

## Why dual problem is important?

The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However the optimal values of the primal and dual problems need not be equal. This understanding will give important insights into the algorithm and solution of optimization problem in linear programming.

**What are the advantages and disadvantages of simplex method?**

Pros of simplex:

- Given n decision variables, usually converges in O(n) operations with O(n) pivots.
- Takes advantage of geometry of problem: visits vertices of feasible set and checks each visited vertex for optimality. (In primal simplex, the reduced cost can be used for this check.)
- Good for small problems.

**When to use simplex method?**

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.

### What is the simplex method?

Simplex Method. The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which is a polytope) in sequence so that at each new vertex the objective function improves or is unchanged.

**What are unbounded solutions in simplex method?**

Under the Simplex Method, an unbounded solution is indicated when there are no positive values of Replacement Ratio i.e. Replacement ratio values are either infinite or negative. In this case there is no outgoing variable.