# OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28

OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-28(a), Exe-28(b), Exe-28(c), Self Revision and Chapter Test.  Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28

 Class: 12th Subject: Mathematics Chapter  : Ch-28 Linear Programming of Section -C
 Board ISC Writer OP Malhotra, SK Gupta, Anubhuti Gangal Publications S.Chand Publications 2020-21

-: Included Topics :-

Exe-28(a)

Exe-28(b)

Exe-28(c)

Self Revision

Chapter Test

### OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28

#### Linear Programming Problem :–

A linear programming problem is one in which we have to find optimal value (maximum or minimum) of a linear function of several variables (called objective function) subject to certain conditions that the variables are non-negative and satisfying by a set of linear inequalities with variables, are sometimes called division variables.

#### Terms related to Linear Programming :-

Objective Function: A linear function z = px + qy (p and q are constants) which has to be maximised or minimised, is called an objective function.

Constraints: The linear inequalities or equations or restrictions on the variables of the linear programming problem are called constraints. The conditions x ≥ 0, y ≥ 0 are called non-negative restrictions.

Optimal Value: The maximum or minimum value of an objective function is known as its optimal value.

Optimisation Problem: A problem, which seeks to maximise or minimise a linear function subject to certain constraints as determined by a set of linear inequalities, is called an optimisation problem.

Feasible Region: The common region determined by all the constraints including non-negative constraints x,y>0 of a linear programming problem is called the feasible region for the problem. The region other than the feasible region is called an infeasible region. The feasible region is always a convex polygon.

Feasible Solutions: Points within and on the boundary of the feasible region represent feasible solutions of the constraints. Any point outside the feasible region is called an infeasible solution.

Optimal Feasible Solution: Any point in the feasible region that gives the optimal value of the objective function is called the optimal feasible solution.

Bounded and Unbounded Region: A feasible region of a system of linear inequalities is said to be bounded, if it can be enclosed within a circle. Otherwise, it is called unbounded.

#### Steps for Applying Corner Point Method :-

Find the feasible region of the linear programming problem and determine its corner points either by inspection or by solving the two equations of the lines intersecting at that point.

Evaluate the objective function z = ax + by at each corner point. Let M and m be, respectively denote the largest and the smallest values of these points.

If the feasible region is bounded, then M and m respectively are the maximum and minimum values of the objective function at corner points.

If the feasible region is unbounded , then
(a) M is the maximum value of objective function z, if the open half plane determined by ax + by > M has no point in common with the feasible region. Otherwise, z has no maximum value.
(b) m is the minimum value of z, if the open half plane determined by ax + by < m has no point in common with the feasible region. Otherwise, z has no minimum value.

### Exe-28(a)

OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28

Exe-28(b)

Exe-28(c)

### Self Revision

OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28

Chapter Test

### OP Malhotra Linear Programming ISC Class-12 Maths Solutions Ch-28

-: End of Linear Programming S. Chand ISC Class-12 Maths Solution :-

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