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Complementary slackness is a condition that provides a relationship between the primal and dual problems. It states that the product of each pair of corresponding primal and dual variables is zero if either variable is non-basic (values at lower bound for minimization, upper bound for maximization).

The duality gap is the difference between the objective function values of the primal and dual problems. For linear programming problems, if both problems are feasible, the duality gap is zero at optimality due to the Strong Duality Theorem.

The Dual Simplex Method is an algorithm used for solving linear programming problems when the dual problem is more convenient to solve. It is especially helpful when a problem has feasible but not optimal solutions, as it iteratively improves the dual solution.

In linear programming, inequality constraints in the primal problem correspond to variable bounds in the dual problem. In the dual problem, less-than-or-equal-to constraints in the primal become variables bounded below by zero in the dual, and greater-than-or-equal-to constraints become variables bounded above by zero.

The Strong Duality Theorem asserts that if the primal problem has an optimal solution, then the dual problem also has an optimal solution, and the optimal values of the objective functions of both primal and dual problems are equal.

Pivot operations in the context of the simplex method involve changing the basis of the linear program to move towards optimality. Each pivot operation in the primal reflects a corresponding operation in the dual, maintaining the complementary slackness condition.

The Weak Duality Theorem states that for any feasible solution to the primal problem, and any feasible solution to the dual problem, the value of the objective function for the dual will always be greater than or equal to that of the primal (assuming a maximization problem).

Sensitivity Analysis in linear programming examines how the optimal solution is affected by changes in the coefficients of the objective function or the right-hand side coefficients of the constraints. It helps in understanding the stability of the optimal solution to the primal and dual problems.

In linear programming, every linear programming problem, referred to as the 'primal problem', can be associated with another problem called the 'dual problem'. The solutions to the primal and dual problems provide bounds for each other.

Biduality refers to the concept that the dual of the dual problem is the primal problem itself. This property ensures that duality in linear programming is symmetric.

Shadow prices, related to dual variables, represent the rate of change in optimal value of the objective function of the primal problem with respect to changes in the right-hand side values of the constraints. They are economic interpretations of the dual solution.