For the primal problem below, write out its matrix form, its dual problem, and the matrix form of the dual problem. Explain why the objective function for the dual problem is minimized. Solve the primal problem and its dual with SAS and write out the optimal solutions and the shadow prices in vector form. Attach all the SAS outputs below. Do not attach the full SAS-screen. If I cannot read your output, the question will receive zero credits.

Primal Problem:

Maximize Z = 2x₁ + 7x₂ + 4x₃,

subject to

x₁ + 2x₂ + x₃ 10

3x₁ + 3x₂ + 2x3 10

and x₁ 0, x₂ 0, x₃ 0.