# NCERT Solutions Class 12 Maths Chapter 12 Exercise 12.1 Linear Programming

NCERT solutions for class 12 maths chapter 12 exercise 12.1 linear programming teaches kids the procedure of solving linear programming questions using two theorems and the corner point method. According to the first theorem, let R be the feasible region (convex polygon) for a linear programming problem and the objective function is given by Z = ax + by. The optimal value (maximum or minimum) of Z must occur at a corner point or vertex of the feasible region, where the variables x and y are subject to constraints described by linear inequalities. The next theorem states that let Z = ax + by being the objective function and let R be the feasible region for a linear programming problem. Then will Z have both a maximum and a minimum value on R, only if R is bounded and each of these values occurs at a corner point (vertex) of R. The class 12 maths NCERT solutions chapter 12 exercise 12.1 has 10 problems that see the use of these two theorems in detail.

While attempting the question in the NCERT solutions class 12 maths chapter 12 exercise 12.1 linear programming students need to keep in mind whether the problem is asking them to minimize or maximize the value of Z. Additionally, they must also shade the correct region in order to get the right solution set. The link is given below can be used to access the scrollable PDF version of the solutions.

**ā** Download NCERT Solutions Class 12 Maths Chapter 12 Exercise 12.1

**Exercise 12.1 Class 12 Chapter 12**

### More Exercises in Class 12 Maths Chapter 12

- NCERT Solutions Class 12 Maths Chapter 12 Ex 12.1
- NCERT Solutions Class 12 Maths Chapter 12 Ex 12.2
- NCERT Solutions Class 12 Maths Chapter 12 Miscellaneous Ex

## NCERT Solutions Class 12 Maths Chapter 12 Exercise 12.1 Steps

The steps to solve the questions in the NCERT solutions class 12 maths chapter 12 exercise 12.1 linear programming using the corner point method are given below:

- Find the feasible region of the linear programming problem.
- Determine its corner points (vertices).
- Find the value of the objective function Z = ax + by at each corner point.
- Let N and n respectively be the largest and smallest values at these points.
- N and n respectively are the maximum and minimum values of the objective function, if the feasible region is bounded. If the feasible region is unbounded, then
- If the open half-plane determined by ax + by > N has no point in common with the feasible region then N is the maximum value of the objective function. Otherwise, the objective function has no maximum value.
- If the open half-plane determined by ax + by < n has no point in common with the feasible region then n is the minimum value of the objective function. Otherwise, the objective function has no minimum value.

NCERT solutions class 12 maths chapter 12 exercise 12.1 gives a detailed description of questions using the above-stated method.

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