Question

The feasible region represented by the given constraints $2x + 3y \ge 12, -x + y \le 3, x \le 4, y \ge 3$ is denoted by

• A. $\text{S}_1$
• B. $\text{S}_2$
• C. $\text{S}_3$
• D. $\text{S}_4$

Hint:

Feasible region = common shaded region satisfying all inequalities.

Answer 1

The Correct Option is C

Concept:
Feasible region = intersection of all inequalities. 

Step 1: Convert inequalities. 
$2x + 3y \ge 12 \Rightarrow$ region above the line 

$-y + x \ge -3 \Rightarrow y \le x + 3$ 

$x \le 4,\quad y \ge 3$ 

Step 2: Plot region.

• Above $2x + 3y = 12$
• Below $y = x + 3$
• Left of $x = 4$
• Above $y = 3$

Step 3: Intersection. 
Common overlapping region gives the feasible region. 

Step 4: Conclusion. 
From standard labeled diagram $\rightarrow \boxed{S_3}$