Funding more than one research team in a R&D project task can increase the chance that at least one of them will achieve a timely breakthrough. However resource limitations imply that the budget allocated to each team declines with the amount of parallelism, reducing the chance that the team will be successful. This tradeoff between level of support and degree of parallelism was explicitly modeled for distinct goals in an environment of uncertain achievements, in order to decide on the number of parallel research teams to fund. In this study which is mainly based on the work done by Gerchak et al, we present the suggested model together with its underlying assumptions and give a detailed mathematical ananlysis. Furthermore, we analytically and numerically analyse the problem of allocating a fixed budget over two research activities and deciding on the number of parallel teams within each activity. Moreover we come out with an analytical result for the general problem of having M activities.