If the optimal value of the objective function $z = px + y$ of an L.P.P occurs at two corner points (2, 11) and (4, 5) of its bounded feasible region, then its optimal value is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 17
Given:
- Objective function: $z = px + y$
- Optimal value occurs at both corner points $(2, 11)$ and $(4, 5)$
Since the optimal value is the same at both points, we equate the values of $z$ at these points:
$z = p(2) + 11 = p(4) + 5$
$\Rightarrow 2p + 11 = 4p + 5$
$\Rightarrow 6 = 2p \Rightarrow p = 3$
Now substitute $p = 3$ into the objective function to find the optimal value:
$z = 3x + y$
At point $(2, 11)$: $z = 3(2) + 11 = 6 + 11 = {17}$