company is a family business that is dedicated to the manufacture of children's furniture. It currently sells three different products s, tables and armchairs. The company wants to determine how much of each of its products to make in order to maximize profit. To do this, is developed the following LP model: number of children's chairs to be manufactured x₂: number of tables for children to be manufactured x3: number of children's armchairs to be manufactured Z: Total profit to be obtained from the manufacture and sale of children's fumitureMax Z = 500x₁ + 600x + 1000x, S.T.: 0.4x₁ + 0.2x₂ +0.5x3 ≤ 120 0.2x₁ +0.2x₂ +0.4x3 ≤ 80 0.2x, +0.4x +0.52590 (Hours available for assembly) (total available capacity) (Cubic meters of wood available) From the previous approach, the following initial table is obtained for the Simplex method: Max X₂ X3 S₁ 5₂ $3 b Z -500 -600 -1000 0 0 0 0 S1 0.4 0.2 0.5 1 0 120 $₂ 0.2 0.2 0.4 0 0 80 0.2 0.4 0.5 10 1 90 The attached table shows the optimal solution of the problem: Max b X3 $₂ X1 $1 33 0 100 Z 0 500 0 1500 195000 -1 0 5 0 150 -5 -0.08 0 -0.2 1 -0.6 2 $2 -2 0 4 120 X3 0 1.2 Using Sensitivity Analysis, determine, by showing ALL calculations (step by step), what is required: a) The company currently has 90 cubic meters of wood to produce. What would be the minimum amount of said resource that could be considered in such a way that the same products continue to be manufactured? Show all necessary formulas and matrix calculations (10 points). b) Given that the current profit for the production and sale of the tables is $600; what is the minimum profit that the company should obtain in order to make this product profitable? Show all necessary formulas and matrix calculations (10 points). 1 0 0 1 0 A