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Using Simplify[Minimize[{term2, b >= c > b/2 >= 0 && a >= d > a/2 >= 0}, {c,d}]] I was able to get the following output:

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I am now wondering how to properly interprete the result. On the left hand side I can see that there are three possible minimized values of the expression. But then, $c$ and $d$ have only two results. Also since, there is the # sign in the $c$ value, what does it mean? Were we able to find a solution or not really? Sorry for asking super basic questions. It's just I couldn't find a nice explanation online.

bajun65537
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    For $c$, the slot signs # are just additional variables in the Root expression - i.e $c$ is the root of that multinomial in variables $a, b, #_1$ – flinty Aug 07 '21 at 11:01
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    See https://mathematica.stackexchange.com/a/126156/4999 for a discussion of Root. – Michael E2 Aug 07 '21 at 13:45
  • I also was lost on which line for the value corresponds to which line of the solution for $c$ and $d$. Since there was a discrepancy in the number of lines (three vs. two). But I think I understand the way Mathematica prints the solutions, I just need to read the conditions right to the solutions more carefully. – bajun65537 Aug 07 '21 at 13:57
  • Each Piecewise expression tells you explicitly the domain for each of its values. Note that when posting questions include all code and data (both in copy and paste-able InputForm) needed to reproduce the results. Without the definition of term2 we cannot produce results that we can read. – Bob Hanlon Aug 07 '21 at 14:52

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