Question

The region represented by the system of inequalities x, y≥0, y≤8, x + y≤4 is:

• A. unbounded in first quadrant
• B. unbounded in first and second quadrant
• C. bounded in first quadrant
• D. bounded in first and second quadrants

Answer 1

The Correct Option is C

The problem involves determining the region represented by a system of inequalities. Let's analyze each inequality step-by-step:

1. First constraint: x, y ≥ 0
   This signifies that the region lies in the first quadrant where both x and y are non-negative.
2. Second constraint: y ≤ 8
   This implies a horizontal line at y = 8 and the region is below this line.
3. Third constraint: x + y ≤ 4
   This is the equation of a line that intersects the axes. Setting x = 0 gives y = 4 and setting y = 0 gives x = 4. Therefore, the line connects the points (0, 4) and (4, 0).

The solution involves finding the overlap of these constraints:

• The intersection of y ≤ 8 and x + y ≤ 4 lies within a triangle formed by the points (0, 0), (0, 4), and (4, 0).

By visualizing these constraints, we see that the bounded region is inside the triangular area limited to the first quadrant. Therefore, the region is bounded in the first quadrant, confirming the possible choices.

Correct selection: bounded in first quadrant