6. For each of the following statements, state whether it is true or false. Just

Question

6. For each of the following statements, state whether it is true or false. Justify your answer (a) An LP in standard form (with m constraints and n variables) that has an optimal solution must have an optimal solution where m of the variables take on positive values. (b) Given an LP in standard form (with m constraints and n variables), any set of m columns will define a legitimate basis. (c) If a BFS for an LP in minimization form is not optimal than the reduced cost of all non-basic variables must be negative (d) If the Simplex method (applied to a minimization problem) reaches a degenerate bfs, then it cannot make an improving move even if there is a non-basic variable with negative reduced cost.

Explanation / Answer

a). True, For all linear programs the decision variable should be greater than or equal to zero.

b). False, The set of constraints should be applicable as per decision variable.

c).False, A basic feasible solution has all components non-negative.

d). True, If there is non basic variable with negative reduced cost then BFS is optimal.

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