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Converting a function composing of multipe pieces into a linear equation

I assume here that the $\beta_j$ are all nonnegative. You can linearize the definition of $b_1$ as follows: $$b_1 \le \beta_1 x_1$$ $$b_1 \le \beta_1 x_2$$ $$b_1 \ge \beta_1 (x_1 + x_2 - 1).$$ The ...
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