Microeconomics.

[Nikkita]

U= e^[(x1+ In x2)^1/3]

Find Optimal values of x1 and x2.

[Nikkita]

( Hint: I think something to be done using the fact that the function is the monotonic transformation of the function U= x1+ In x2)

[Econ17]

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[Abhitesh]

Monotonic transformation will greatly simplify. But it can be solved directly.
Let the budget line be p*x1+x2=m. And [(x1+lnx2)^1/3] = z or [{(m-x2)/p + lnx2}^1/3]=z.
Then dU/dx2 = 0 => dU/dz * dz/dx2 = 0.
dU/dz being exponential function cannot be zero.
So dz/dx2 = 0.