NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.2

CBSE NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.2 in Hindi and English Medium updated for 2022-2023 free PDF and Videos. Download Class 12 Maths Offline app or Class 12 Ganit Offline app free.

The term linear implies that all mathematical relations used in the problem are linear relations, while the term programming refers to the method of determining a particular program or action plan. Before continuing, we now formally define some terms (which have been used before) that we will use in linear programming problems Objective function. The linear function Z = ax + by, where a, b are constants that must be maximized or minimized is called the linear objective function.

Constraints: Inequalities or equations or constraints on variables in a linear programming problem are called constraints. The conditions x conditions 0, and are 0 are called nonnegative inhibitions. Groups of inequalities are bottlenecks. A problem that attempts to maximize or minimize a linear function (according to two variables x and y) subject to some constraints set by a set of linear inequalities is called an optimization problem. Linear programming problems are a special type of optimization problems.

The graph of the LPP (shaded region) includes points common to all half-planes determined by oddities. Each point in this field represents a possible option for the dealer to invest. This area is called the possible area for the problem. Each point in this area is called a possible solution to the problem. The common area determined by all the constraints, including the non-negative constraints x, y of 0, of a linear programming problem is called the possible area (or solution area) of the problem. Any point in the possible region that gives the optimal (maximum or minimum) value of the objective function is called the optimal solution.

Theorem 1: Let R be the possible area (convex polygon) for a linear programming problem and let Z = ax + b and objective function. When Z has an optimal value (maximum or minimum), where the x and y variables are subject to the constraints described by linear inequalities, this optimal value must be at a corner point (top) of the possible region.
Theorem 2: Let R be the possible field for a linear programming problem and let Z = ax + b as an objective function. If R is bounded, the maximum and minimum values of the objective function Z are R and each of them is at a corner point (vertex) of R.