Read the following scenarios example 1 and 2:

Example 1. A company manufactures two products, tables and chairs. The sales volume of the tables is at least 80% of the total sales of tables and chairs. However, the company cannot sell more than 100 table units per day. Both products use a raw material, whose maximum daily availability is 240 lbs. The raw material consumption rates are 2 lbs per unit of tables and 4 lbs per unit of chairs. Tables and chairs profits are $200.00 and $500.00, respectively.

1.- Determine the optimal mix of products for the company to maximize its profits.

Example 2:

Minimize 2A + 2B

Subject to: 1A + 3B 12

3A + 1B 13

1A - 1B = 3

A, B 0

1.- Determine the optimal solution using the simplex method.

2.- Through algebraics, determine the maximum number of basic solutions or corner points.

3.- Corroborates the optimal solution, obtained with the simplex method, through the data table with the algebraic one.

4.- Based on the results, it provides an interpretation of these.