Straight Lines question bank (Mathematics)

The maximum value of z = 6x +8y subject to $x-y\ge 0,x+3y\le 12,x\ge 0,y\ge 0$ is…..

$\triangle \mathrm{OAB}$ is formed by the lines $x^2-4 x y+y^2=0$ and the line $A B$. The equation of line $A B$ is $2 x+3 y-1=0$. Then the equation of the median of the triangle drawn from the origin is