The minimum value for the LPP $\mathrm{Z}=6 x+2 y$, subject to $2 x+y \geq 16, x \geq 6, y \geq 1$ is
The minimum value for the LPP $\mathrm{Z}=6 x+2 y$, subject to $2 x+y \geq 16, x \geq 6, y \geq 1$ is
$44$
$47$
$24$
$34$
Solution
Here $\mathrm{A}(8,0), \mathrm{B}(0,16)$ lie on $2 \mathrm{x}+\mathrm{y}=16$ When $y=1, x=\frac{15}{2} \quad$ i.e. $E\left(\frac{15}{2}, 1\right)$
When $x=6, y=4 \quad$ i.e. $F(6,4)$
$Z(E)=6 \times \frac{15}{2}+2 \times 1=47$
$Z(F)=6 \times 6+2 \times 4=36+8=44$
