JEE Main & Advanced Mathematics Linear Programming Terms of Linear Programming

The term programming means planning and refers to a process of determining a particular program.

(1) Objective function : The linear function which is to be optimized (maximized or minimized) is called objective function of the L.P.P.

(2) Constraints or Restrictions : The conditions of the problem expressed as simultaneous equations or inequations are called constraints or restrictions.

(3) Non-negative constraints : Variables applied in the objective function of a linear programming problem are always  non-negative. The inequations which represent such constraints are called non-negative constraints.

(4) Basic variables : The \[m\] variables associated with columns of the \[m\times n\] non-singular matrix which may be different from zero, are called basic variables.

(5) Basic solution : A solution in which the vectors associated to m variables are linear and the remaining \[(n-m)\] variables are zero, is called a basic solution. A basic solution is called a degenerate basic solution, if at least one of the basic variables is zero and basic solution is called non-degenerate, if none of the basic variables is zero.

(6) Feasible solution : The set of values of the variables which satisfies the set of constraints of linear programming problem (L.P.P) is called a feasible solution of the L.P.P.

(7) Optimal solution : A feasible solution for which the objective function is minimum or maximum is called optimal solution.

(8) Iso-profit line : The line drawn in geometrical area of feasible region of L.P.P. for which the objective function (to be maximized) remains constant at all the points lying on the line, is called iso-profit line.

If the objective function is to be minimized then these lines are called iso-cost lines.

(9) Convex set : In linear programming problems feasible solution is generally a polygon in first quadrant. This polygon is convex. It means if two points of polygon are connected by a line, then the line must be inside the polygon. For example,

(i) and (ii) are convex set while (iii) and (iv) are not convex set.