Consider the following linear programming problem:

Min 15x1 + 64x2 − 6x3 − 6x4 − 8x5 

s.t. x1 + 8x2 − x3 − 2x4 − x5 = 0 

x1 − x2 − 3x3 − x4 = −1 

x1 , x2 , x3 , x4 , x5 ≥ 0

(a) Derive its dual linear programming problem.

(b) Solve the dual problem by using the graphic method.

(c) Write down the Complementary Slackness conditions for this LP problem.

(d) Use (c) to find an optimal solution to the primal problem.