Question

The feasible region represented by the constraints \(y-2x\leq 4,x+y\geq 5,x\leq 4,y\geq 2,x,y\geq 0\) is ...........

• A. a convex bounded region with 4 corner points
• B. an unbounded region
• C. a convex bounded region with 5 corner points
• D. no feasible region

Hint:

Find the corner points by pairing boundary lines.

Answer 1

The Correct Option is A

Step 1: Sketch the bounds:
Lower bound $y\ge2$ and $y\ge5-x$; upper bound $y\le 2x+4$; right bound $x\le4$.

Step 2: Lower boundary:
The lower boundary is $y = 5 - x$ from $x = \tfrac13$ to $x = 3$, then $y = 2$ from $x=3$ to $x=4$.

Step 3: Count vertices:
Corners: $(\tfrac13,\tfrac{14}3)$, $(3,2)$, $(4,2)$, $(4,12)$. That is four, and the region is closed, so option (A).

Final Answer:
The feasible region is bounded with 4 corner points. \[ \boxed{\text{(A) }\text{convex bounded region with 4 corner points}} \]