Let \(a,\) \(b,\) \(c,\) and \(d\) be positive real numbers such that \(36a + 4b + 4c + 3d = 25.\) Find the maximum value of \(a \times \sqrt{b} \times \sqrt[3]{c} \times \sqrt[4]{d}.\)
\(\text{This one I'd do using Lagrange multipliers}\\ f(a,b,c,d) = a \cdot \sqrt{b} \cdot \sqrt[3]{c} \cdot \sqrt[4]{d}\\ g(a,b,c,d) = 36a+4b+4c+3d-25\\ \text{Solve}\\ \nabla(f-\lambda g) = 0\)
