Each of the following is a linear program with no optimal solution. State the corresponding dual, solve both primal and dual graphically, and verify that whenever primal or dual is unbounded, the other is infeasible.

(a) max 4x1 + x2 s.t. 2x1 + x2 Ú 4 3x2 … 12 x1, x2 Ú 0

(b) max 4x1 + 8x2 s.t. 3x2 Ú 6 x1 + x2 … 1 x1, x2 Ú 0

(c) min 10x1 + 3x2 s.t. x1 + x2 Ú 2

-x2 Ú 5 x1, x2 Ú 0

(d) min x1 - 5x2 s.t. - x1 + x2 … 4 x1 - 5x2 … 3 x1, x2 Ú 0

(e) min - 3x1 + 4x2 s.t. - x1 + 2x2 Ú 2 x1 - 2x2 Ú 5 x1, x1 Ú 0

(f) max -20x1 + 15x2 s.t. 10x1 - 2x2 … 12

-10x1 + 2x2 … -15 x1, x2 Ú 0