Questions to solve:
Use the simplex method to solve the following exercises.
1. Maximize z = 4x1 + 2x2
Subject to -x1 - x2 ≤ 12
3x1 - x2 ≤ 15
x1 ≥ 0, x2 ≥ 0.
2. Maximize z = 5x1 + 4x2 + x3
Subject to -2x1 + x2 + 2x3 ≤ 3
x1 - x2 + x3 ≤ 1
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
Please describe how you found the answer to each problem using the simplex method.