Can I really factor a constant into the $\min$ function? Say I have $\min(5x_1,x_2)$ and I multiply the whole function by $10$, i.e. $10\min(5x_1,x_2)$. Does that simplify to $\min(50x_1,10x_1)$? In one of my classes I think my professor did this but I'm not sure (he makes very hard to read and seemingly bad notes), and I'm just trying to put these notes together. Thanks!

Ys, that is legal as long as the constant is not negative. I.e., $10 \cdot \max(3, 5) = 10 \cdot 5 = 50$ is the same as $\max(10 \cdot 3, 10 \cdot 5) = 50$, but try multiplying by $-10$... 
