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Binary variables $Y_i$ are introduced to model the activation status of each machine. They take the value 1 if machine $i$ is used and 0 otherwise.

Conditions: The problem involves machines with fixed setup costs.; Production quantities are continuous variables.; The goal is to minimize total cost including both variable and fixed components.

Binary variables $Y_i$ are introduced to model the activation status of each machine. They take the value 1 if machine $i$ is used and 0 otherwise.

Conditions: The problem involves machines with fixed setup costs.; Production quantities are continuous variables.; The goal is to minimize total cost including both variable and fixed components.

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.