In a linear programming problem (LPP), the maximum value of the objective function \(Z = 2x + 5y\) subjected to the constraints: \(2x + 3y \le 6,\ 2x + y \le 4,\ x, y \ge 0\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10
The feasible region is bounded, so the maximum occurs at a corner point. The lines \(2x + 3y = 6\) and \(2x + y = 4\) meet where (subtracting the second from the first)
\(2y = 2,\quad y = 1,\quad x = \frac{3}{2}\)
The corner points are (0, 0), (2, 0) on \(2x + y = 4\), \(\left(\frac{3}{2}, 1\right)\) and (0, 2) on \(2x + 3y = 6\). Values of Z:
\(Z(0, 0) = 0\)
\(Z(2, 0) = 4\)
\(Z\left(\frac{3}{2}, 1\right) = 3 + 5 = 8\)
\(Z(0, 2) = 10\)
The maximum value is 10, at (0, 2).