NCERT Solutions for Class 12 Maths chapter 12-Linear Programming Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter-12 Linear Programming

NCERT solutions for class 12 maths Chapter-12 Linear Programming is prepared by academic team of Physics Wallah. We have prepared  NCERT Solutions for all exercise of chapter-12. Given below is step by step solutions of all questions given in NCERT textbook for Chapter-12.

NCERT Solutions for Class 12 Maths Miscellaneous Exercise

Solve The Following Questions.

Question1. Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

Solution :

Let the diet contain x and y packets of foods P and Q respectively. Therefore,

x ≥ 0 and y ≥ 0

The mathematical formulation of the given problem is as follows.

Maximize z = 6x + 3y … (1)

subject to the constraints,

4x + y ≥80       .......(2)

x + 5y ≥ 115     .....(3)

3x + 2y ≤ 150   ......(4)

x,y ≥ 0            ......(5) 

The feasible region determined by the system of constraints is as follows.

The corner points of the feasible region are A (15, 20), B (40, 15), and C (2, 72).

The values of z at these corner points are as follows.

Thus, the maximum value of z is 285 at (40, 15).

Therefore, to maximize the amount of vitamin A in the diet, 40 packets of food P and 15 packets of food Q should be used. The maximum amount of vitamin A in the diet is 285 units.