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# help

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Let $$a,$$  $$b,$$ $$c,$$ and $$d$$ be positive real numbers such that $$36a + 4b + 4c + 3d = 25.$$ Find the maximum value of $$a \times \sqrt{b} \times \sqrt[3]{c} \times \sqrt[4]{d}.$$

Apr 9, 2019

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$$\text{This one I'd do using Lagrange multipliers}\\ f(a,b,c,d) = a \cdot \sqrt{b} \cdot \sqrt[3]{c} \cdot \sqrt[4]{d}\\ g(a,b,c,d) = 36a+4b+4c+3d-25\\ \text{Solve}\\ \nabla(f-\lambda g) = 0$$

Apr 9, 2019

$$\text{This one I'd do using Lagrange multipliers}\\ f(a,b,c,d) = a \cdot \sqrt{b} \cdot \sqrt[3]{c} \cdot \sqrt[4]{d}\\ g(a,b,c,d) = 36a+4b+4c+3d-25\\ \text{Solve}\\ \nabla(f-\lambda g) = 0$$