Question

Sketch the region {(x, y): x ≥ 0, y ≥ 0, x + 2y ≤ 4} in a coordinate system set up by you.

Answer 1

Given inequality x + 2y ≤ 4

i ) Take x + 2y = 4

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| x | 0 | 4 |
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| y | 2 | 0 |
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Plotting ( 0 , 2 ) , ( 4 , 0 ) on the graph

and join them , we get a line x + 2y = 4 .

ii ) To find the region x + 2y ≤ 4 ,

substitute ( 0 , 0 ) in the inequality,

we get

0 ≤ 4 ( True )

Shade the region which contains ( 0,0 )

Therefore ,

Shaded region shows x + 2y ≤ 4

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