Question

10.3x+4y560, x +3y30,120. У20

Answer 1

The inequalities are,

3x+4y ≤ 60, x+3y ≤ 30, x ≥ 0, y ≥ 0.

For the inequality,

3x+4y ≤ 60(1)

Put the value, x=0 in equation (1).

3( 0 )+4y = 60 4y = 60 y = 15

Put the value, y = 0 in equation (1).

3x+4( 0 ) = 60 3x = 60 x= 20

For the inequality,

x+3y ≤ 30(2)

Put the value, x=0 in equation (2).

( 0 )+3y = 60 3y = 60 y = 20

Put the value, y = 0 in equation (2).

x+3( 0 ) = 30 x = 30

For the inequality x ≥0, the value of x can be equal to 0or greater than 0.

For the inequality y ≥0, the value of y can be equal to 0or greater than 0.

For all the four inequalities, the graph is shown as:

In the graph, the inequality x ≥0 is shown by green color, the inequality y ≥0 is shown by black color, the inequality x+3y≤ 30 is shown by red color and the inequality 3x+4y ≤ 60 is shown by blue color.

Thus, the region ABDC as shown in the graph is the graph of the system of all four inequalities.