A company produces two types of alloys, each composed of three metals in different proportions: copper, zinc, and lead. The company holds an inventory of each type of metal. The sale price of alloy i (i = 1, 2) is denoted by pi. The company has an inventory of metal type j (j = 1, 2, 3) of sj units. The proportion of metal j present in alloy i is of aji. The company wishes to produce xi units of each alloy type in such a way that its revenue is maximized

Please solve by applying the simplex method in vector matrix form and show all steps. I appreciate any help, I am so lost with this subject.

\begin{tabular}{|c|c|c|c|} \hline Metal / Alloy & Alloy 1 & Alloy 2 & Inventory \\ \hline Copper & 0.4 & 0.5 & 300 units \\ Zinc & 0.3 & 0.4 & 200 units \\ Lead & 0.3 & 0.1 & 150 units \\ \hline Alloy Price & $1500 & $1800 & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|} \hline Metal / Alloy & Alloy 1 & Alloy 2 & Inventory \\ \hline Copper & 0.4 & 0.5 & 300 units \\ Zinc & 0.3 & 0.4 & 200 units \\ Lead & 0.3 & 0.1 & 150 units \\ \hline Alloy Price & $1500 & $1800 & \\ \hline \end{tabular}