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in Basic Algebra by (49.3k points)
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Determine the region in the plane determined by the inequalities:

3x +4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0

1 Answer

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Best answer

The given inequality is 3x + 4y ≤ 60. 

Draw the graph of the line 3x + 4y = 60. 

Table of values satisfying the equation 

3x + 4y = 60

x 8 12
y 9 6

Putting (0, 0) in the given inequation, we have 3 × 0 + 4 × 0 ≤ 60 ⇒ 0 ≤ 60, which is true. 

∴ Half plane of 3x + 4y ≤ 60 is towards origin. 

Also the given inequality is x + 3y ≤ 30. 

Draw the graph of the line x + 3y = 30. 

Table of values satisfying the equation . 

x + 3y = 30

x 0 9
y 10 7

Putting (0, 0) in the given inequation, we have 0 + 3 × 0 ≤ 30 ⇒ 0 ≤ 30, which is true. 

∴ Half plane of x + 3y ≤ 30 is towards origin.

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