Problem $3(30$ points$)$:

SarFarm Oil Company produces three types of vegetable oils $-$ soybean oil, canola oil, and sunflower oil$-$under a contract with Seed's Market. Under this agreement, Seed's Market will accept the entire supply of oil delivered by SarFarm Oil Company. The production process involves seed cleaning, oil extraction, and bottling. SarFarm employs $30$ workers in the seed cleaning department, $36$ in the oil extraction department, and $10$ in the bottling department. The factory operates on an $8-$hour shift, $5$ days a week. The following table provides the time requirements and profits per unit for the three oils.

$\backslash$table$[[$Hours Per Unit,Cleaning,Extraction,Bottling,Profit $($$$/$Unit$)],[$Oil$,2,6,1,4],[$Soybean$,4,4,2,5],[$Canola$,1\mathrm{.}5,3,1\mathrm{.}5,3],[$Sunflower$,,,,]]$

What is the best weekly production schedule for SarFarm?

a$)$ Formulate the LP in canonical form. Indicate the decision variables, identify the meaning of each constraint and formulate the objective function. Then, formulate it into standard form $(15$ points$).$

b$)$ Solve the LP using Simplex Method. Indicate all steps and intermediate tableaus $(15$ points$).$