NCERT Solutions for Class 12 Mathematics Chapter 12 Linear Programming

Short Note:

• A linear programming problem (LPP) involves an objective function (a linear function to be maximized or minimized) subject to a set of linear constraints, usually expressed as inequalities.

• Decision variables in an LPP typically represent quantities to be determined and are restricted to non-negative values, reflecting real-world limitations like production quantities or resource usage.

Short Note:

• For problems involving two variables, each constraint is plotted as a line on a graph, and the feasible region is the common region satisfying all constraints simultaneously.

• The feasible region can be bounded (enclosed within a finite area) or unbounded (extending infinitely in some direction), which affects whether a maximum or minimum value definitely exists.

Short Note:

• According to the fundamental theorem of linear programming, the optimal value of the objective function occurs at one of the corner points (vertices) of the feasible region.

• The corner point method involves evaluating the objective function at each vertex of the feasible region and comparing the results to identify the maximum or minimum value.