The feasible region for an LPP is shown in the given figure.

The maximum value of the objective function $z=3x+4y$ is :

100

The correct answer is Option (2) → 100

Coordinator of B = ?

Equation of line ⇒ y = Slope (x) + c

Slope of line = $\frac{y_2-y_1}{x_2-x_1}$

Slope of line $AD=\frac{0-50}{25-0}=-2$

Slope of line $BC=\frac{0-20}{40-0}=-\frac{1}{2}$

Equation of line AD ⇒ $y=-2x+c$

$y=-2x+50$   ...(1)

Equation of line BC ⇒ $y=-\frac{1}{2}x+c$

$20=-\frac{1}{2}(0)+c$

$20=c$

$∴y=-\frac{1}{2}x+20$   ...(2)

From (1) and (2)

$y=-2x+50$

$y=-\frac{1}{2}x+20$

$0=-\frac{3}{2}x+30$

$0=-3x+60$

$x=20$

$y=-2(20)+50$

$=10$

∴ Coordinator of B ⇒ (20, 0)

∴ Maximum value = 100