AM-GM inequality

[wild tiger]

I don't get how to frame the inequality

Let a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of a^5×b^3×c^2×d is 3750β, then the value of β is

[lost kernel]

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[barren crane]

well, notice that (a/5)^5(b/3)^3(c/2)^2(d) is just a scalar multiple of the quantity you are trying to maximize

[wild tiger]

Gotcha

Thank youu