The feasible region for an LPP is given by the following graph

The maximum value of the objective function $Z=4x+10y$ is :

30

The correct answer is Option (1) → 30

The objective function, $Z=4x+10y$

The equation of both the lines is,

$y=mx+c$

$y=\frac{-6}{4}x+c_1$

$2y=-3x+2c_1$

$2y+3x-2c_1=0$

satisfies at (4, 0)

$0+12-2c_1=0$

$c_1=6$

$≡2y+3x-12=0$   ...(1)

$y=-\frac{3}{6}x+c_2$

$2y=-x+2c_2$

$2y+x-2c_2=0$

satisfies at $(6,0)$

$0+6-2c_2=0$

$c_2=3$

$≡2y+x-6=0$   ...(2)

$⇒2x-6=0$

$x=3,y=\frac{3}{2}$

$Z(3,\frac{3}{2})=4×3+10×\frac{3}{2}$

$=12+15=27$

$Z_{max}(0,3)=4×0+10×3=30$