Working on a problem of comparative advantage of the economist David Ricardo, I've gone into solving a more general case of that study in which I stumbled over this question : how do we maximize the quantity $P = ax + by + c$, given that $a, b$ and $c$ are all known and $x, y$ are variables confined to the interval $[ 0,T] $.
In short, my query is : Determine $(x,y) \in [0,T]^2$ such that $(ax + by + c)$ is maximal, with $(a,b,c) \in \mathbb{R}^3$, all of which are known.
Thank you !
Assuming $a, b \neq 0$, use these four statements to get the maximum:
If $a$ is negative, $x=0$.
If $a$ is positive, $x=T$.
If $b$ is negative, $y=0$.
If $b$ is positive, $y=T$.
"Do. Or do not. There is no try." ~Yoda