NCERT Solutions for Class 12 Maths Chapter 12 Miscellaneous Exercise 12 in English Medium and Hindi Medium PDF file with videos, updated for CBSE academic session 2022-2023. These solutions are useful for UP Board and other state boards also, who are using NCERT Books for their course.

## Class 12 Maths Chapter 12 Miscellaneous Exercise

### Class 12 Maths Chapter 12 Miscellaneous Exercise in English and Hindi

Class: 12 | Mathematics |

Chapter: 12 | Linear Programming Problems LPP |

Miscellaneous Exercise 12 | Hindi and English Meidum |

CBSE NCERT Solutions for Class 12 Maths Chapter 12 Miscellaneous Exercise 12 in PDF and Videos format free to use in Hindi or English Medium. Download Class 12 Maths Offline App in English or Class 12 Ganit App in Hindi.

### Class 12 Maths Chapter 12 Miscellaneous in Video

##### Corner search method

The method consists of the following steps:

- Find the feasible area of the linear programming problem and determine its vertices (vertices) by inspection or by solving two equations of lines intersecting at that point.
- Evaluate the objective function Z = ax + at each corner. Let m and m, respectively, be the largest and smallest values of these points.
- (i) When there is a range of possible area, M and m are the maximum and minimum values of Z.

(ii) If the potential field is not constrained, we have: - (a) M is the maximum 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 maximum value.

(b) Similarly, 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.

#### What is corner point?

A corner point of a potential field is a point in the area that is the intersection of two boundary lines. It is said to be a possible region of a system of linear inequalities, if it can be enclosed within a circle. Otherwise it is called unlimited. Unlimited means that the possible field extends indefinitely in either direction.

###### Different Types of Linear Programming Problems

**Manufacturing Problems**: In these problems, we determine the number of units of different products that a company must produce and sell when each product requires a certain labor force, machine hours, labor hours per product, warehouse space to get maximum profit, production per unit etc.**Dietary problems**: In these problems, we determine the amount of various components / nutrients, which should be included in a diet to reduce the cost of the desired diet so that each component / nutrient component contains one Contains a fixed minimum quantity.**Transportation Issues**: In these issues, we set the transport schedule to find the cheapest way of transporting the product from the plants / factories located in different markets in different places.

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