This paper examines the computability of optimal power allocation strategies for utility maximization and maxmin fairness. It is demonstrated that a computable constraint power function exists. However, when both total and individual power constraints are taken into account, it is determined that the optimal power allocation for maximizing network utility is not computable since every single power value is a non-computable number. Furthermore, it is established that within the same constraint context, both the max-min fairness level and its corresponding power values are non-computable numbers.