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in Linear Programming by (29.6k points)
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Solve graphically :

x + 2y ≤ 6

1 Answer

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Best answer

Consider the line whose equation is x + 2y = 6.

To find the points of intersection of this line with the coordinate axes.

Put y = 0, we get x = 6.

∴ A = (6, 0) is a point on the line. 

Put x = 0, we get 2y = 6, i.e. y = 3 

∴ B = (0, 3) is another point on the line.

Draw the line AB joining these points. This line divide the line into two parts.

1. Origin side 

2. Non-origin side

To find the solution set, we have to check the position of the origin (0, 0) with respect to the line.

When x = 0, y = 0, then x + 2y = 0 which is less than 6.

∴ x + 2y ≤ 6 in this case.

Hence, origin lies in the required region. Therefore, the given inequality is the origin side which is

shaded in the graph.

This is the solution set of x + 2y ≤ 6.

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