\section*{Exercise 2 - 091012}

In each of three companies I, II, III, three products \(E_{1}, E_{2}, E_{3}\) were produced. The production costs per unit were the same for identical products in all three companies. The table below shows the daily quantities of the produced products as well as the daily total production costs.

\begin{tabular}{l|l|l|l|l}
\hline Company & \multicolumn{2}{|l|}{ Daily Quantities } & Daily Total Production Costs in M \\
& \(E_{1}\) & \(E_{2}\) & \(E_{3}\) & \\
\hline I & 5 & 5 & 8 & 5950 \\
II & 8 & 6 & 6 & 6200 \\
III & 5 & 8 & 7 & 6450 \\
\hline
\end{tabular}

What were the production costs per unit for each of the product types?
Let \(p_{i}\) be the production costs for \(E_{i}\), then we have

\[
5 p_{1}+5 p_{2}+8 p_{3}=5950 \quad(1) ; \quad 8 p_{1}+6 p_{2}+6 p_{3}=6200 \quad(2) ; \quad 5 p_{1}+8 p_{2}+7 p_{3}=6450
\]

Solving the system of linear equations yields: \(p_{2}=300, p_{3}=400\) and \(p_{1}=250\).