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y 2 x 0 2x y 4

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y>-2, x>0, 2x+y<4

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Answer to a math question y>-2, x>0, 2x+y<4

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Hank

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101 Answers

Solution:
1. Given constraints:
-

y > -2

x > 0

2x + y < 4

2. Analyze the constraints:
- The inequality

y > -2

represents the region above the horizontal line

y = -2

.
- The inequality

x > 0

represents the region to the right of the vertical line

x = 0

.
- The inequality

2x + y < 4

can be rearranged to

y < -2x + 4

, representing the region below the line

y = -2x + 4

.

3. Graph the lines and identify the solution region:
- The intersection of these regions in the coordinate plane forms the valid solution region.
- The solution region is above the line

y = -2

, to the right of the line

x = 0

, and below the line

y = -2x + 4

.

4. Conclusion: The feasible region is in the first quadrant, bounded by the lines

y = -2

and

y = -2x + 4

when

x > 0

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