Diagonalization of matrices, classification of quadratic forms, and linear programmingMain objectivesThe objective of this activity is to consolidate your learning about linear applications and diagonalization.In addition, a linear programming problem will be modeled using systems of linear inequalities and their associated matrix, and the solution will be proposed using the simplex algorithm.Description of the activity and instructionsThe activity consists of four exercises, with several sections each one that you will have to solve.The exercises must be solved showing the solving process. It will not be evaluated if the student only presents the solution of the exercise without explaining how he/she has reached the result.

Task 3. Linear programming and simplex algorithm. 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 assembiy, 3 and 6 kg of enamel for painting, and 14 and 10 hours of quality control. Activities College Mathematics |l {code MAC1014} The total manufacturing costs per unit are, respectively, 30 and 23, and the selling prices 52 and 48, all in hundreds of euros. The entrepreneur has 4500 hours for assembly, 8 400 000 grams of enamel and 20 000 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. l Transform the model by adding the necessary slack variables to meet the constraints. r- Solve it using the simplex method. Interpret the optimal solution including the slack variables