Question

The common region of the solution of the inequations $x+y \ge 5$, $y \le 4$, $x \ge 2$, $x, y \ge 0$ is

• A. unbounded and non-origin side
• B. unbounded and origin side
• C. bounded and origin side
• D. bounded and non-origin side

Hint:

Whenever a linear programming question contains a constraint specifying a variable is greater than a positive value (like $x \ge 2$) without a corresponding upper bound line (like $x \le k$), the region will almost always extend infinitely along that axis, making it unbounded!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Analyze the feasible region defined by x≥0, y≥0, x≥2, y≤4, x+y≥5 for boundedness and origin side.

Step 2: Key Formula or Approach:
Test origin (0,0) in x+y≥5; examine if any constraint limits x to a finite maximum.

Step 3: Detailed Explanation:
Origin test: 0≥5 (False) → non-origin side. With x≥2 and no upper bound on x, the region extends infinitely rightward → unbounded.

Step 4: Final Answer:
The region is unbounded and on the non-origin side, matching option (A).