ML Aggarwal Linear Programming ISC Class-12 APC Maths

ML Aggarwal Linear Programming ISC Class-12 Understanding APC Maths Solutions Chapter-3 of Section-C. Step by step Solutions of ML Aggarwal ISC Understanding APC Mathematics Class-12 Exercise Questions with Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

ML Aggarwal Linear Programming ISC Class-12 Understanding APC Maths Solutions Chapter-3

Class: 12th
Subject: Mathematics
Chapter : Ch-3 Linear Programming  Section-C
Board ISC Board
Writer ML Aggarwal ISC Understanding ( Vol-II)
 Publications APC Arya Publications ( 2020-21 )

-: Select Topics :-

Exercise-3.1 

Exercise-3.2

Chapter Test


ML Aggarwal Linear Programming ISC Class-12 Understanding APC Maths Solutions

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.

Fundamental Theorems for Solving Linear Programming

  • Theorem 1: Let R be the feasible region for a linear programming problem and let z = ax + by be the objective function. When z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities. This optimal value must occur at a corner point (vertex) of the feasible region.
    Note: A corner point of a feasible region is a point in the region which is the intersection of two boundary lines.
  • Theorem 2: Let R be the feasible region for a linear programming problem and let z = ax + by be the objective function. If R is bounded, then z has both a maximum and a minimum value on R and each of these recurs at a corner point of JR.
    Note: Maximum or a minimum may not exist,- if the feasible region is 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.


Exercise –3.1

ML Aggarwal Linear Programming ISC Class-12 Understanding APC Maths Solutions

(page-1478)

Question 1: Two tailor A and B earn 300 and 400 per day ……….. formulate this as an LPP.

Question 2: A small firm manufacture necklace and bracelets. The total number of necklace and ………… of each must be produced.

Question 3:  A furniture delear deals in only two items – table and chairs. He has ………… he can maximum profit.


Exercise –3.2

ML Aggarwal Linear Programming ISC Class-12 Understanding APC Maths Solutions

(page-1503 to 1506)

Question 1: Maximum Z = 3x + 4y, subject to the constraints x + y ≤ 4, x ≥ 0, y ≥ 0.

Question 2: Minimum Z = -3x + 4y subject to the constraints x + 2y ……… 0.

Question 3: ………………….
…………………..

Question 32: An oil company has two depots A and B with capacities of 7000 litre and 4000 litre ……………… given in following data.

…………………


Chapter Test

ML Aggarwal Linear Programming ISC Class-12 Understanding APC Maths Solutions

(page-1507 to 1508)

Question 1: Maximum Z = 8x + 7y, subject  to the constraints ………… 0.

Question 2: A company manufacture two types of screw A and b. All the screw have ………. LPP and solve graphically.

Question 3: …………………..

……………………

Question 9: Two godowns A and B have a grain stroge capacity of 100 ………. shops are given in the following table :

-: End of Linear Programming ML Aggarwal ISC Class-12 Solutions :-

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6 thoughts on “ML Aggarwal Linear Programming ISC Class-12 APC Maths”

  1. Hey I’m in 12th this year and wanna completely understand the concept of this . Your website was really helpful but since you locked the content it take time to find solution on other websites . I request you please me and let us use the content that you provided .

    Reply
    • dear student / well wisher / Teacher
      the previous version of 2020-21 has been removed because council has decided to start new session from 1st April Therefore we are upgrading the solutions of 2021-22 editions
      Sorry for inconvenience
      thanks
      team icsehelp

      Reply
  2. It’s been a month we can’t find solutions on other websites . please keep the goodwork
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