Given the following linear programming problem:
Maximize z = 5x₁ + 6x₂
Subject to:
x₁ + 2x₂ = 5
-x₁ + 5x₂ ≥ 0
4x₁ + 7x₂ ≥ 8
x₁ unrestricted, x₂ ≥ 0
Assuming yₜ, i = 1, 2, 3 as the dual variables associated with constraints 1, 2, and 3 respectively.
The objective function of the dual problem is:
A. minimize z = 5y₁ + 6y₂
B. minimize z = 5y₁ + 8y₃
C. minimize z = 2y₁ + 5y₂ + 7y₃
D. minimize z = 5y₁ + 5y₂ + 8y₃
E. None of the above
