In this paper we present an algorithm to solve an as-yet untreated knapsack problem, the Multidimensional Multiple-choice Knapsack Problem (MMKP). Since our specific application occurs in the real-time domain, a solution for the MMKP with a small upper bound on the runtime is desirable. Thus, the Lagrange multiplier method is chosen, and a heuristic with a worst-case runtime behavior better than O(n2m) is developed, n being the number of elements and m the number of dimensions. Extensive testing against an exact algorithm based on partial enumeration is used to establish the accuracy and efficiency of the heuristic.