For the given linear programming problem \(z = ax + by, a, b \gt 0\) subject to the constraints \(2x + y \le 10, x + 3y \le 15, x, y \ge 0\). If the corner points are (0, 0), (5, 0), (3, 4) and (0, 5) and \(z\) is maximum at both (3, 4) and (0, 5), then the relationship between \(a\) and \(b\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(b = 3a\)
If z is maximum at two corner points, it takes the same value at both:
\(z(3, 4) = z(0, 5)\)
\(3a + 4b = 5b\)
\(b = 3a\)
With \(b = 3a\) this common value \(15a\) is indeed the maximum, since \(z(5, 0) = 5a\) and \(z(0, 0) = 0\) are smaller.
NCERT Exemplar:
Linear Programming
