In the context of linear programming problem, duality implies that each linear

programming problem can be analyzed using two different ways which have

equivalent solutions.

If the primal contains $n$ variables and $m$ constraints; the dual will contain $m$

variables and $n$ constraints.

The maximization problem in the primal becomes the maximization problem

in the dual and vice versa.

The coefficient matrix of the constraints of the dual is the transpose of the

primal.

The methods of solving the dual linear programming are not similar with that

of the original linear programming problems.

Sensitivity analysis is concerned with the study of 'sensitivity' of the optimal

solution of LP problem with changes in parameters.

In transportation problem, the sum of allocations along each row equals the

supply of each row and the sum of the allocations down each column equals the

demand or requirement of each column.

In general, transportation model is used for cost maximization problems.

The assignment problem has many applications in allocations and scheduling.

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Critical path analysis is commonly used with all forms of projects.