Classify the Following Problems as to Whether They Are Pure-Integer,mixed-Integer,zero-One,goal,or

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