The feasible region of an LPP is in the form of a parallelogram as shown in the figure. If the objective function is $Z=3 x+4 y$ and maximum value is 82, at what coordinates does it attain the maximum value?

(14, 10)

The correct answer is Option (3) → (14, 10)

$Z=3x+4y$

$\text{Maximum of a linear objective function occurs at a vertex}$

$3x+4y=82$

$\text{Checking integer feasible vertex satisfying this:}$

$x=14,\;\; y=10 \Rightarrow 3(14)+4(10)=82$

The maximum occurs at $(14,10)$.