The minimum value of \(Z = 2x + y\) subjected to \(x + y \ge 10,2x + 3y \le 26, x, y \ge 0\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 14
The feasible region lies on or above the line x + y = 10, on or below the line 2x + 3y = 26, and in the first quadrant.
The two lines meet where
\(2x + 3(10 - x) = 26\)
\(x = 4,\quad y = 6\)
On the x-axis, x + y = 10 gives (10, 0) and 2x + 3y = 26 gives (13, 0). The feasible region is the triangle with corner points (4, 6), (10, 0) and (13, 0). The value of Z at each corner:
\((4, 6):\ Z = 8 + 6 = 14\)
\((10, 0):\ Z = 20\)
\((13, 0):\ Z = 26\)
The region is bounded, so the minimum value is 14, at (4, 6).