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The area of the feasible region for the following constraints 3y + x ≥ 3, x ≥ 0, y ≥ 0 will be
- a)bounded
- b)unbounded
- c)convex
- d)concave
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The area of the feasible region for the following constraints 3y + x &...
Given constraints are 3y + x ≥ 3, x ≥ 0, y ≥ 0
Let ,
l1: 3y+x=3
l2: x = 0
l3: y = 0
The corner points are A(0,1), B(3,0) So, from the graph, we can say that the area of the feasible region is unbounded.
Let ,
l1: 3y+x=3
l2: x = 0
l3: y = 0
The corner points are A(0,1), B(3,0) So, from the graph, we can say that the area of the feasible region is unbounded.
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The area of the feasible region for the following constraints 3y + x &...
In order to determine the area of the feasible region for the given constraints, we need to first graph the inequalities and find the intersection points.
The constraints are:
1) 3y ≤ x
2) y ≤ 4
3) y ≥ 2
4) x ≥ 0
Let's start by graphing the lines for each constraint:
1) 3y ≤ x:
To graph this inequality, we can rewrite it in slope-intercept form:
y ≤ (1/3)x
2) y ≤ 4:
This is a horizontal line at y = 4.
3) y ≥ 2:
This is a horizontal line at y = 2.
4) x ≥ 0:
This is a vertical line at x = 0 (y-axis).
Now, let's plot these lines on a graph and find the intersection points. The feasible region is the area where all the constraints are satisfied.
After graphing the lines, we find that the feasible region is a triangle with vertices at (0, 2), (0, 4), and (12, 4). To calculate the area of the triangle, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 12 * 2
Area = 12
Therefore, the area of the feasible region for the given constraints is 12 square units.
The constraints are:
1) 3y ≤ x
2) y ≤ 4
3) y ≥ 2
4) x ≥ 0
Let's start by graphing the lines for each constraint:
1) 3y ≤ x:
To graph this inequality, we can rewrite it in slope-intercept form:
y ≤ (1/3)x
2) y ≤ 4:
This is a horizontal line at y = 4.
3) y ≥ 2:
This is a horizontal line at y = 2.
4) x ≥ 0:
This is a vertical line at x = 0 (y-axis).
Now, let's plot these lines on a graph and find the intersection points. The feasible region is the area where all the constraints are satisfied.
After graphing the lines, we find that the feasible region is a triangle with vertices at (0, 2), (0, 4), and (12, 4). To calculate the area of the triangle, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 12 * 2
Area = 12
Therefore, the area of the feasible region for the given constraints is 12 square units.
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