The corner points of the bounded feasible region for an LPP are (0, 20), (3, 12), (6, 8), and (0, 15).The objective function is $Z= αx + βy$, where $α, β> 0$. If the maximum of Z occurs at the corner points (3, 12) and (6, 8), then the relationship between $α$ and $β$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $α =\frac{4}{3}β$
Given corner points: (0, 20), (3, 12), (6, 8), (0, 15)
Objective function: Z = αx + βy, with α, β > 0
Maximum occurs at (3, 12) and (6, 8).
For the objective function to have the same value at these two points:
Z(3, 12) = Z(6, 8)
α(3) + β(12) = α(6) + β(8)
3α + 12β = 6α + 8β
12β - 8β = 6α - 3α
4β = 3α
$\frac{α}{β } = \frac{4}{3}$