Let the corner points of the bounded feasible region of the linear programming problem (LPP) \(Z = ax+by\) be (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between \(a\) and \(b\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2a = 5b\)
When the optimal value occurs at two corner points, Z has the same value at both points:
\( \displaystyle 2a + 0 \cdot b = \frac{20}{19}a + \frac{45}{19}b \)
Multiplying by 19:
\(38a = 20a + 45b\)
\(18a = 45b\)
\(2a = 5b\)