Convex mathematical programing is proposed as a method of optimally allocating forest inventory sampling resources under different sampling plans to meet specified precision requirements on several variables. Results of a sensitivity analysis under sampling with partial replacement shows the response of the solution to changing inputs when each restriction becomes limiting. The solutions illustrate that the optimum replacement fraction can vary from complete remeasurement to large replacement fractions depending upon the specified precision levels, the population parameters, and the relative costs of obtaining information. Forest Sci. 20:117-127.