Tropicalization $min(2x,2y,0)$ is a piecewise linear function.

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Please instruct me on how to interpret $min(2x,2y,0)$ as a piecewise linear function.

I have been working up to it for a while because I really wanted insight towards computing blowups in algebraic geometry... according to nlab though it is also useful in mirror symmetry problems... if I don't find out here what else should I try!!!

Library notes: I couldn't figure out how to optimize the function along the planes like advised to me in the comment section. 1/4 2/4 3/4 4/4