An objective function \(z = ax + by\) is maximum at points (15, 15) and (0, 20). If \(a, b \ge 0\) and \(ab = 27\), then the maximum value of the objective function is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 180
Since z is maximum at both points, it has the same value at both points:
\(15a + 15b = 0 \cdot a + 20b\)
\(15a = 5b\)
\(b = 3a\)
Using \(ab = 27\):
\(3a^2 = 27,\quad a^2 = 9\)
\(a = 3\) (as \(a \ge 0\)), \(b = 9\)
The maximum value is
\(z = 20b = 20 \times 9 = 180\)