The solution of LPP :

Min.(z)= 100x+ 400y

s.t. $x+2y ≥8$

$2x+5y≤20$

$x≥0, y≥0.$

occurs at :

$x=8, y = 0 $

Given LPP:

Minimize $Z=100x+400y$

Subject to

$x+2y\ge 8$

$2x+5y\le 20$

$x\ge 0,\;y\ge 0$

Thus feasible corner points are $(8,0)$ and $(0,4)$.

Evaluate $Z$:

$Z(8,0)=100(8)+400(0)=800$

$Z(0,4)=100(0)+400(4)=1600$

Minimum value is $800$.

final answer: minimum occurs at $(8,0)$