As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function $z = 2x + y$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10 **
The feasible region (from the shaded area in the graph) has the following corner points:
$A(0,1),\; B(1,0),\; D(2,4),\; C\left(\frac{10}{3},\frac{10}{3}\right)$
Objective function: $z = 2x + y$
Evaluate $z$ at each corner:
At $A(0,1)$: $z = 2(0)+1 = 1$
At $B(1,0)$: $z = 2(1)+0 = 2$
At $D(2,4)$: $z = 2(2)+4 = 8$
At $C\left(\frac{10}{3},\frac{10}{3}\right)$:
$z = 2\cdot\frac{10}{3} + \frac{10}{3} = \frac{30}{3} = 10$
Maximum value = $10$