The notion of duality within linear programming asserts that every linear program has associated with it a related linear program called its dual. The original problem in relation to its dual is termed the primal. 24. any of the deep geometric insight behind linearprogrammingduality. The main goal is to explain in detail the mechanical procedure of taking the dual. Linear case. Linear programming problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is a linear combination of n variables. There are m constraints, each of which places an upper bound on a linear combination of the n variables. Solve a simple linear program defined by linear inequalities. see Interior-Point-Legacy LinearProgramming.) duality gap, or total relative