Task $3.$ ?Provide a step by step with working for question

An entrepreneur intends to manufacture two types of freezers named A and $B.$ ?Each

of them must go through three operations before being marketed: Assembly,

painting and quality control.

Freezers A and $B$ ?require, respectively, $150$ ?and $180$ ?minutes of assembly, $3$ ?and $6kg$

of enamel for painting, and $14$ ?and $10$ ?hours of quality control.

The total manufacturing costs per unit are, respectively, $30$ ?and $28,$ ?and the selling

prices $52$ ?and $48,$ ?all in hundreds of euros.

The entrepreneur has $4500$ ?hours for assembly, $8400000$ ?grams of enamel and

$20000$ ?hours for quality control per week.

Formulate a linear programming model indicating how many freezers must be

produced of each type for maximum profit, taking into account the demand study.

Transform the model by adding the necessary slack variables to meet the

constraints.

Solve it using the simplex method. Interpret the optimal solution including the

slack variables.