# Maximize profit of a chemical plant

A chemical plant makes three major products on a weekly basis. Each of these products requires a certain quantity of raw chemical and different production times, and yields different profits. The pertinent information is given in Table 1. Note that there is sufficient warehouse space at the plant to store a total of 450kg/week.

                Product I   Product II    Product III   Resource Availability
Raw Chemical       7kg          5kg           5kg              3000kg
Production Time 0.05h/kg      0.1h/kg       0.2h/kg           55h/week
Profit           $30/kg$30/kg        \$35/kg


Table I: Datasheet of the three major products of the company.

Set up a linear programming problem to maximize profit and solve it using Simplex Method (manually), along with a graph and a MATLAB code to solve the problem using Simplex Method (with comments) with an algorithm/pseudocode for the same.

I recently started studying Linear Programming, and I don't know where to study from. I have tried checking several books, but I do not know how to approach such practical questions. I do not know how I should solve this question normally, and forming a Linear Programming Model, is tending to be too difficult for me. Also, I do not know how I should solve such questions using MATLAB, or any other mathematical software in general. Could anyone please help me out in this question?

I would appreciate a step-by-step solution, or some guidance in solving such practical questions in future. Also, could anyone recommend me a book for practical Linear Programming questions like these?