Mathematics - Area Under Curves Question with Solution | TestHub

We have,$z=ax+by,a,b>0$
Subject to constraints$x\le 2,y\le 2,x+y\ge 3x,y\ge 0$
On taking given constraints as equation, we get the following graph

Here, ABCA is the required feasible region whose corner points are$A\left(\mathrm{2,1}\right),B\left(\mathrm{1,2}\right)$and$C\left(\mathrm{2,2}\right)$.
Since, It is given that$z=ax+by;a,b>0$
has minimum value at$\left(\mathrm{2,1}\right)$
$\therefore$Value of z at$\left(\mathrm{2,1}\right)<$value of z at$\left(\mathrm{1,2}\right)$
$\Rightarrow 2a+b<a+2b$
$\Rightarrow a<b$