To maximize the function u(x, y) = x^α * y^β under the constraint Ax + By = m, the method of Lagrange multipliers is recommended as an effective approach. Alternatively, one can express y in terms of x using the constraint, leading to a single-variable function. The next steps involve differentiating this function with respect to x and setting the first-order condition (FOC) to zero to find critical points. The user is struggling with deriving the FOC correctly and seeks assistance in solving it. Understanding these steps is crucial for identifying candidate solutions and checking the second-order conditions for maxima.
