Operations Research or Qualitative Approach MCQ Questions and Solutions with Explanations | Management

Any column or raw of a simplex table is called a vector. The simplex method, in mathematical optimization, is a well-known algorithm used for linear programming.

If there are ‘m’ original variables and ‘n’ introduced variables, then there will be 3 + m + n columns in the simplex table.

A minimization problem can be converted into a maximization problem by changing the sign of coefficients in the objective functions. A minimization problem is in standard form if the objective function is to be minimized, subject to the constraints where.

If in a LPP , the solution of a variable can be made infinity large without violating the constraints, the solution is unbounded. 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.

In the Big M method of linear programming, artificial variables are introduced to obtain an initial basic feasible solution when a straightforward starting solution is not available.

To ensure that these artificial variables are driven out of the solution during the optimization process, a large penalty is associated with them.

In maximization problems, a large negative value (–m) is assigned to the artificial variables in the objective function.

This discourages their presence in the optimal solution since including them would significantly reduce the value of the objective function.

Therefore, –m is the correct coefficient to assign to artificial variables in maximization cases.

In simplex method, we add artificial variable variables in the case of ‘=’. In order to use the simplex method on problems with mixed constraints, we turn to a device called an artificial variable. This variable has no physical meaning in the original problem and is introduced solely for the purpose of obtaining a basic feasible solution so that we can apply the simplex method.

In simplex method, if there is tie between a decision variable and a slack (or surplus) variable, Decision variable should be selected. A decision variable is a quantity that the decision-maker controls.

A BFS of a LPP is said to be degenerate if at least one of the basic variable is zero. A basic feasible solution is called degenerate if value of at least one basic variable is zero.

In LPP, degeneracy occurs in two stages. Degeneracy in a linear programming problem is said to occur when a basic feasible solution contains a smaller number of non-zero variables than the number of independent constraints when values of some basic variables are zero and the Replacement ratio is same.

Every LPP called the primal is associated with another LPP called dual. Either of the problems is primal with the other one as dual.