Chapter 6.7, Problem 7P

Program Plan Intro

Dual of Linear Programming(LP):

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

• Every variable in the primal Linear Programming becomes a constraint in the dual LP.
• Every limit in the primal Linear Programming becomes a variable in the dual LP.
• In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Weak Duality:

• The weak duality is an optimization concept that states that the gap in duality is always greater than or equal to 0.
• This means the solution to the primary(minimization) problem is always greater than or equal to the solution to a dual problem associated with it.

Explanation of Solution

b.

Validity of the form of Lemma 3:

For showing validity of form of Lemma 3, it need to show that the dual is feasible and this will imply that the primal is bounded.

Assuming that the dual is to be feasible, let ${\text{y}}_{\text{0}}$ be a dual feasible point with a $\text{w-value}$ of ${\text{w}}_{\text{0}}$.

Then Weak Duality implies that $[\text{Obj}$