Classify the Following Problems as to Whether They Are Pure-Integer

Essay

Classify the following problems as to whether they are pure-integer, mixed-integer, zero-one, goal, or nonlinear programming problems.
(a)Maximize Z = 5 X1 + 6 X1 X2 + 2 X2
Subject to: 3 X1 + 2 X2 ≥ 6
X1 + X2 ≤ 8
X1, X2 ≥ 0
(b)Minimize Z = 8 X1 + 6 X2
Subject to: 4 X1 + 5 X2 ≥ 10
X1 + X2 ≤ 3
X1, X2 ≥ 0
X1, X2 = 0 or 1
(c)Maximize Z = 10 X1 + 5 X2
Subject to: 8 X1 + 10 X2 = 10
4 X1 + 6 X2 ≥ 5
X1, X2 integer
(d)Minimize Z = 8 X12 + 4 X1 X2 + 12 X22
Subject to: 6 X1 + X2 ≥ 50
X1 + X2 ≥ 40