# Operation Research: system of equations

I have a system of equations for my Operations Research class, and the book is solving them by using algebra. However, I think it would be easier to solve them using linear algebra, and will also serve as a powerful tool. The only problem the system has is that it is has constraints. Here is the system:

$Z = 3 x_1 + 5 x_2$, where $Z$ is the total profit. $$\begin{cases} 1 x_1 + 0 x_2 \leq 4 \\ 0 x_1 + 2 x_2 \leq 12 \\ 3 x_1 + 2 x_2 \leq 18 \end{cases}$$ Also, $x_1$ and $x_2$ are $\geq 0$.

Answer: $x_1 = 2$,
$x_2 = 6$ and
$Z = 36$.

How would I solve it using linear algebra? Thanks

Instead of an inquality use equality by adding a variable $u,v,w\ge 0$ s.t : $$x_1 + u = 4$$ $$2x_2+ v = 12$$ $$3x_1+2x_2+w = 18$$