How to solve the following system of linear inequalities?

Question

How to solve the following system of linear inequalities in $x$, $y$ and $z$?

$$x\ge\frac{y+z}{1.9}$$ $$y\ge\frac{x+z}{2.25}$$ $$z\ge\frac{x+y}{1.6}$$ $$x,y,z\ge0$$

I'm an amateur at math.

Answer 1

You should use the Simplex Algorithm. I hope you have some kind of mathematical toolbox at your disposal (excel should do it). But you basically should rewrite your problem in the form:

$$ Av=0 $$ $$ v_i \geq0 \, (\forall i) $$

To assemble the $A$ matrix and $v$ vector : $$ x\geq \frac{y+z}{1.9} \Rightarrow 1.9x -y-z \geq0 \Rightarrow 1.9x -y-z +t_1=0 \, (t_1 \geq0) $$

So the first line of $A$ is $[1.9, -1,-1,1,0,0]$. @Dr. Sonnhard Graubner already pointed a solution.