Question

Consider the following feasible region. Which of the following constraints represents the feasible region ?

A. 2x + 3y ≤ 6
B. x - 2y ≤ 2
C. 3x + 2y ≤ 12
D. 3x - 2y ≤ -3
E. x - 2y ≥ -1
Choose the correct answer from the options given below :

• A. A, C and E only
• B. B, D and E only
• C. B and C only
• D. A, B and D only

Answer 1

The Correct Option is C

The problem is to determine which constraints represent the feasible region shown in the image. Let's analyze each option:

• Option A: 2x + 3y ≤ 6
  This inequality represents a line, and to verify if it is part of the feasible region, test a point from the region, like (0,0). The calculation would be:
  2(0) + 3(0) = 0 ≤ 6, which is true. Check another point like (3,0) which yields:
  2(3) + 3(0) = 6 = 6, true on the inequality line.
  This constraint seems plausible.
• Option B: x - 2y ≤ 2
  Test point: (0,0):
  0 - 2(0) = 0 ≤ 2, true.
  Test point: (2,0):
  2 - 2(0) = 2 ≤ 2, also true.
  This constraint fits the feasible region.
• Option C: 3x + 2y ≤ 12
  Test point: (0,0):
  3(0) + 2(0) = 0 ≤ 12, true.
  Test point: (4,0):
  3(4) + 2(0) = 12 = 12, true on the boundary line.
  This constraint marks an edge of the region.
• Option D: 3x - 2y ≤ -3
  Test point: (0,0):
  3(0) - 2(0) = 0 ≤ -3, false.
  This is not part of the feasible region.
• Option E: x - 2y ≥ -1
  Test point: (0,0):
  0 - 2(0) = 0 ≥ -1, true.
  This constraint could also be a part of the edge.

After verifying, constraints B and C correctly describe the feasible region based on testing points and the orientation of the lines. Therefore, the correct answer is B and C only.