Solve: Primal LP and Optimal
Consider the following primal LP:
Max Z = -4x_1 - x_2
S.t.
4x_1 + 3x_2 >= 6
x_1 _ 2x_2 =< 3
3x_1 + x_2 = 3
x_1, x_2 >= 0
a) Find the dual to this primal LP and its optimal solution.
b) If we changed primal LP to:
Max Z = -4x_1 - x_2 - x_3
S.t.
4x_1 + 3x_2 + x_3 >= 6
x_1 + 2x_2 _ x_3 =< 3
3x_1 + x_2 + x_3 = 3
x_1, x_2, x_3 >= 0
would the current optimal solution remain optimal?