Decision Variables, Determine Decision Variables: Let X 1 be the number of private

Decision Variables

Determine Decision Variables:

Let X₁ be the number of private homes to be inspected
Let X₂ be the number of office buildings to be inspected
Let X₃ be the number of industrial plants to be inspected

Objective Function

Max Z = X₁ + X₂ + X₃

With subject to Constraints

(1) X₁ + X₂ + X₃ ≤ 0.6X1 (private homes must be at least 60% of the total inspections)
This can be rewritten as 0.4X1 + X2 + X3 ≤ 0

(2) X₂ ≥ 8 (minimum requirement for offices)
(3) X₃ ≥ 8 (minimum requirement for plants)
(4) 2X₁ + 4X₂ + 6X₃ ≤ 120 (electrical inspection)
(5) X₁ + 3X₂ + 3X₃ ≤ 80 (gas inspection)
(6) 3X₁ + 2X₂ + X₃ ≤ 100 (electrical inspection)
(7) X_i ≥ 0 (non-negativity)

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