Each of the following LP has a finite optimal solution. State the corresponding dual, solve both primal and dual graphically, and verify that optimal objective function values are equal.

(a) max 14x1 + 7x2 s.t. 2x1 + 5x2 … 14 5x1 + 2x2 … 14 x1, x2 Ú 0

(b) min 4x1 + 10x2 s.t. 2x1 + x2 Ú 6 x1 Ú 1 x1, x2 Ú 0

(c) min 8x1 + 11x2 s.t. 2x1 + 9x2 Ú 24 3x1 + x2 Ú 11 x1, x2 Ú 0

(d) max 7x1 s.t. 4x1 + 2x2 … 7 3x1 + 7x2 … 14 x1, x2 Ú 0