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The linking constraint $X_i \le C_i Y_i$ enforces the on/off production rule by scaling the capacity limit $C_i$ with the binary activation variable $Y_i$. When the machine is active ($Y_i=1$), the constraint becomes $X_i \le C_i$, allowing production up to the full capacity.

Conditions: $X_i$ is the production quantity on machine $i$.; $Y_i$ is the binary activation indicator for machine $i$.; $C_i$ is the maximum capacity of machine $i$.; $X_i \ge 0$ is enforced.

The linking constraint $X_i \le C_i Y_i$ enforces the on/off production rule by scaling the capacity limit $C_i$ with the binary activation variable $Y_i$. When the machine is active ($Y_i=1$), the constraint becomes $X_i \le C_i$, allowing production up to the full capacity.

Conditions: $X_i$ is the production quantity on machine $i$.; $Y_i$ is the binary activation indicator for machine $i$.; $C_i$ is the maximum capacity of machine $i$.; $X_i \ge 0$ is enforced.

The total cost objective function is constructed by summing the variable production costs and the fixed setup costs. Variable costs are calculated by multiplying the unit variable cost of each machine by the number of units produced on that machine ($X_i$).

Conditions: There are multiple machines with distinct variable and fixed costs.; $X_i$ represents the continuous production quantity on machine $i$.; $Y_i$ represents the binary activation status of machine $i$.; The goal is cost minimization.

The total cost objective function is constructed by summing the variable production costs and the fixed setup costs. Variable costs are calculated by multiplying the unit variable cost of each machine by the number of units produced on that machine ($X_i$).

Conditions: There are multiple machines with distinct variable and fixed costs.; $X_i$ represents the continuous production quantity on machine $i$.; $Y_i$ represents the binary activation status of machine $i$.; The goal is cost minimization.