Give the system of equations A mining company produce in three mines aluminium and zinc. At the following matrix give the information about the amount of zinc and alluminium at a produced tonne of ore and the corresponding cost per tonne of ore: 
$$\begin{matrix}
\text{Mine } & \text{ Zinc } & \text{ Alluminium } & \text{ Cost/ tonne of ore }\\ 
1 & 10\% & 40\% & 60\\ 
2 & 20\% & 30\% & 45\\ 
3 & 30\% & 20\% & 40
\end{matrix}$$ 
For a specific costumer 100 t of zinc and 200 t of alluminium have to be produced.  We have to give a system of equations, from which the required amounts for the production at each mine  can be computed. We have to give also all the solutions of this system. 
I have done the following but I am not really sure if I understood correctly the exercise... 
Let $z_i$ be the amount of zinc produced by the mine $i$ and let $a_i$ be the amount of alluminium produced by the mine $i$.
Then do we get the following system? 
$$0.1x_1+0.2x_2+0.3x_3=100 \\ 0.4a_1+0.3a_2+0.2a_3=200$$ 
Is this correct? 
 A: What the problem statement says is that for mine $i $, each tone of ore is $x_i \%$ zinc and $y_i \% $ alluminium, for the tabled values.
Hence if mine $i $ produces $t_i $ tones of ore we have $x_it_i $ zinc and $y_it_i $ alluminium because from each ton of ore, we can extract both zinc and alluminium.
Therefore your system is not quite right yet.
Can you make it right? Also, what is the cost, in terms of the tons extracted from each mine, to fulfill that order?
You may want to start by assuming each mine produced $t_i $ tons of ore and then calculating how much zinc and how much alluminium that makes up.
Using your own table, we have
$$\begin{matrix}
\text{Mine } & \text{ Zinc } & \text{ Alluminium } & \text{ Cost/ tonne of ore }\\ 
1 & 10\% & 40\% & 60\\ 
2 & 20\% & 30\% & 45\\ 
3 & 30\% & 20\% & 40
\end{matrix}$$ 
so we just rename the 1st, 2nd and 3rd columns to
$$\begin{matrix}
\text{(Mine)}\ i & x_i & y_i & \text{ Cost/ tonne of ore }\\ 
1 & 10\% & 40\% & 60\\ 
2 & 20\% & 30\% & 45\\ 
3 & 30\% & 20\% & 40
\end{matrix}$$ 
Therefore if, for example, mine 1 produces $10$ tons of ore, $t_1 = 10$, we have $x_110 = 0.1\cdot10 = 1$ ton of zinc.
We now say that mines 1, 2 and 3 produced $t_1, t_2$ and $t_3$ tons of ore. We can write this table:
$$\begin{matrix}
\text{Tons produced in mine}\ i & \text{ Amount of zinc } & \text{ Amount of alluminium } & \text{ Total cost of production }\\ 
t_1 & x_1t_1 & y_1t_1 & t_160\\ 
t_2 & x_2t_2 & y_2t_2 & t_245\\ 
t_3 & x_3t_3 & y_3t_3 & t_340
\end{matrix}$$ 
But we need that the total zinc produced be $100$ tons and the total alluminium be $200$ tons therefore we must have:
$$
\begin{cases}
x_1t_1 + x_2t_2 + x_3t_3 = 100\\
y_1t_1 + y_2t_2 + y_3t_3 = 200
\end{cases}$$
