- #1
Mr Davis 97
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Homework Statement
If ##A,B,C,D## are positive numbers such that ##A+2B+3C+4D = 8##, then what is the maximum value of ##ABCD##?
Homework Equations
The Attempt at a Solution
From AM-GM, I know that the maximum is ##2/3##. However, I want to know exactly what A,B,C, and D must be to take on this maximum. From AM-GM, I know that it must be the case that A=2B=3C=4D for equality to occur, but I'm not sure how I can use this explicitly, as a four-way equality is unwieldy.