When a limited amount of effort is available for the performance of two related tasks, the practical of how it is to be divided between them in order to obtain the best over-all result is one which constantly arises in operations research. The object of the present paper is to show how the question can often be put in quantitative form, and then to give it a simple mathematical solution in illustrative cases, interpreting the results in the language of recommended procedures. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.