Consider the linear-programming problem:

Maximize z = 2x₁ + x₂ + 3x₃ + x₄,

subject to:

x₁ + x₂ + x₃ + x₄ <= 5,

2x₁ - x₂ + 3x₃ = -4,

x₁ - x₃ + x₄ >= 1,

x_1, x₃ >= 0, x₂ and x₄ unrestricted.

(a) State this problem with equality constraints and nonnegative variables.

(b) Write the dual to the given problem and the dual to the transformed problem found in part (a). Show that these two dual problems are equivalent.

Thank you!