The maximum value of \(z = 5x + 7y\) subjected to constraints \(x + y \le 5, x \ge 0, y \ge 0\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 35
The feasible region is the triangle bounded by \(x + y = 5\) and the two axes, with corners (0, 0), (5, 0) and (0, 5). On a bounded feasible region, the maximum of z occurs at a corner point:
\((0, 0):\ z = 0\)
\((5, 0):\ z = 25\)
\((0, 5):\ z = 35\)
The maximum value is 35, at (0, 5).