The sum of the $x$ coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y ≤ 14, x≥4, x≤8, y ≥0$ is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
Given constraints:
$x + y \le 14$, $x \ge 4$, $x \le 8$, $y \ge 0$
Find the corner points of the feasible region.
1. From $x = 4$ and $y = 0$ → point (4, 0)
2. From $x = 8$ and $y = 0$ → point (8, 0)
3. From $x = 4$ and $x + y = 14$ → $y = 10$ → point (4, 10)
4. From $x = 8$ and $x + y = 14$ → $y = 6$ → point (8, 6)
Corner points: (4, 0), (8, 0), (4, 10), (8, 6)
Sum of x-coordinates = 4 + 8 + 4 + 8 = 24
Final Answer:
24