Optimal budget allocation when response is S-shaped

We consider the profit maximizing allocation of a budget among n activities when the revenue from each activity is an S-shaped function of the budget allocated to it. Results are obtained for functions that cross only in the convex part. A simple computational procedure based on these results is presented. The results are specialized to cases where the functions do not cross, are multiples of the same function, are identical, and are piecewise linear.