Question

For any primal problem and its duel

Option 1:
Optimal value of objective function is same

Option 2:
Dual will have an optimal solution if primal does to

Option 3:
Primal will have an optimal solution if dual does to

Option 4:
Both primal and dual cannot be infeasible​

Answer 1

Answer:

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Answer 2

Primal will have an optimal solution if dual does to.

Primal and dual-

1) Duality in linear programming states that each linear programming problem is related to another linear programming problem and can therefore be derived from it.

2) The original linear programming problem is called "principal" and the derived linear problem is called "dual".

3) Before solving the duality, we need to formulate the original linear programming problem in standard form.

4) The canonical form means that all variables in the problem must be non-negative, and the symbols '≥', '≤' are used for minimizing and maximizing respectively.

5) The dual of a given linear program (LP) is another LP derived from the original (original) LP in the following schematic way.

6) All variables of the primary LP become constraints of the dual LP.

7) All constraints of the primary LP become variables of the dual LP.

8) The direction of the objective lens is reversed. The primal maximum becomes the dual minimum and vice versa.

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