Question 993888
a+b+c=10, find the maximum value possible for (a*b*c)+(a*b)+(b*c)+(a*c).
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Using Excel, I confirmed my suspicion that the max is at a = b = c
Max = 69967/999
= 31*61/27
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27 is obviously 3*3*3, but I don't know the significance of 31 or 61.
I don't yet have a proof, either.