3. Solve this problem using the simplex method:
Objective function: Maximize 7x₁ + 2x₂
Constraints:
1/2 x₁ + 3x₂ ≤ 12
x₁ ≤ 10
4x₁ - 2x₂ ≥ -5
x₁, x₂ ≥ 0
4. Use the simplex technique to find the optimal solution to this problem:
Objective function: Maximize 5x₁ + 2x₂
Constraints:
x₁ + x₂ ≤ 50
3x₁ + x₂ ≥ 10
x₂ = 10
x₁, x₂ ≥ 0