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An equality constraint is used because the customer order requires exactly 1000 units to be supplied. The problem specifies that the order must be met precisely, meaning neither underproduction (shortfall) nor overproduction (surplus) is permitted.

Conditions: The problem involves fulfilling a specific customer order.; The order quantity is fixed and must be met exactly.; Overproduction or underproduction is not allowed or desired.

An equality constraint is used because the customer order requires exactly 1000 units to be supplied. The problem specifies that the order must be met precisely, meaning neither underproduction (shortfall) nor overproduction (surplus) is permitted.

Conditions: The problem involves fulfilling a specific customer order.; The order quantity is fixed and must be met exactly.; Overproduction or underproduction is not allowed or desired.

Capacity constraints must be linked to binary variables to ensure logical consistency between machine activation and production. Simple capacity limits ($X_i \le C_i$) allow production even if the machine is not activated ($Y_i=0$), which would incur variable costs without paying the fixed setup cost.

Conditions: Machines have fixed setup costs.; Production is bounded by machine capacity.; Binary variables indicate machine activation.; The model must prevent production on inactive machines.

Capacity constraints must be linked to binary variables to ensure logical consistency between machine activation and production. Simple capacity limits ($X_i \le C_i$) allow production even if the machine is not activated ($Y_i=0$), which would incur variable costs without paying the fixed setup cost.

Conditions: Machines have fixed setup costs.; Production is bounded by machine capacity.; Binary variables indicate machine activation.; The model must prevent production on inactive machines.