This is my lecture notes on An Introduction to Functional Analysis.
Clement V. Durrell Readable Relativity G. Bell & Sons Ltd. 1926
This is one of questions from the course Principles of Economics with Calculus.
Suppose that the United States military is fighting two wars at the same time. The wars are taking place in two fronts, A and B. Consider the problem of a general who has to decide how to allocate $M$ units of troops among the two fronts. Based on a recent analysis, the general knows that the benefit of placing a units of troops in front A is $10ln(a)$ and the benefit of placing b units of troops in front B is $20ln(b)$.
QUESTION. What is the expression for the optimal amount of troops that should be placed in front A? (Ignore indivisibility/integer problems by assuming that soldiers can be allocated fractionally to both fronts).