Which of the following are NLP problems, and why?
(a) Maximize profit = 3X1 + 5X2 + 99X3
Subject to X1 ≥ 10
X2 ≤ 5
X3 ≥ 18
(b) Maximize cost = 25X1 + 30X2 + 8X1 X2
Subject to X1 ≥ 8
X1 + X2 ≥ 12
0.0005X1 – X2 = 11
(c) Maximize Z = P1d1– + P2d2+ + P3+
Subject to X1 + X2 + d1– – d1+ = 300
X2 + d2– – d2+ = 200
X1 + d3– – d3+ = 100
(d) Maximize profit = 3X1 + 4X2
X12 – 5X2 ≥ 8
3X1 + 4X2 ≥ 12
(e) Maximize cost = 18X1 + 5X2 + X22
Subject to 4X1 – 3X2 ≥ 8
X1 + X2 ≥ 18
Are any of these quadratic programming problems?