KC Sinha Solution Class 12 Chapter 31 Linear Programming (रैखिक प्रोग्रामन) Exercise 31.1 (Q1-Q8)

 Exercise 31.1

TYPE-I

Solve the following linear inequations graphically :

Question 1

3x-4y<12

Sol :

Question 2

$-3 x+2 y \geq 6$

Question 3

$x+y \leq 0$

Sol :

Question 4

$y \geq-\frac{x}{2}$

Sol :

TYPE-II

Solve the following system of linear inequations graphically :

Question 5

$3 x+4 y \leq 60, x+3 y \leq 30, x \geq 0, \quad y \geq 0$

Sol :

Question 6

$x+3 y \leq 12,3 x+y \leq 12, x \geq 0, y \geq 0$

Sol :

Question 7

$x+y<6,7 x+4 y \leq 28, x \geq 0, \quad y \geq 0$

Sol :

Question 8

Show that the solution set of the following linear inequations is empty :

$x+2 y \leq 3,3 x+4 y \geq 12, x \geq 0, \quad y \geq 1$

Sol :