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) Xi ≥ 0 (non-negativity)