Consider the following problem.
Maximize Z = 2x1 + 7x2 + 4x3
subject to
x1 + 2x2 + x3 ≤ 10
3x1 + 3x2 + 2x3 ≤ 10
x1, x2, x3 ≥ 0.
(a) Construct the dual problem for this primal problem.
(b) Use the dual problem to demonstrate that the optimal value of Z for the primal problem cannot exceed 25.