The sum of the \(x\) coordinates of the corner points of the feasible region for the LPP: Minimize \(z = 3x + 2y\) subject to constraints \(x + y \le 14, x \ge 4, x \le 8, y \ge 0\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
The feasible region lies between the vertical lines \(x = 4\) and \(x = 8\), above the x-axis and below the line \(x + y = 14\). Its corner points are where these boundary lines meet:
\(x = 4,\ y = 0\): \((4, 0)\)
\(x = 8,\ y = 0\): \((8, 0)\)
\(x = 8,\ x + y = 14\): \((8, 6)\)
\(x = 4,\ x + y = 14\): \((4, 10)\)
Sum of the x-coordinates:
\(4 + 8 + 8 + 4 = 24\)
The objective function is not needed: the corner points depend only on the constraints.