Consider the following set of constraints:
X1 + 2x2 + 2x3 + 4x4 ≤ 40
2x1 - x2 + x3 + 2x4 ≤ 8
4x1 + 2x2 + x3 - x4 ≤ 10
X1, x2, x3, x4 ≥ 0
Solve the problem for each of the following objective functions.
(a) Maximize z = 2x1 + x2 + 3x3 + 5x4.
(b) Maximize z = 8x1 + 6x2 + 3x3 - 2x4.
(c) Maximize z = 3x1 - x2 + 3x3 + 4x4.
(d) Minimize z = 5x1 - 4x2 + 6x3 - 8x4.