Optimize me!

[the_fantastic_ms_fox]

I'm going to take a break from homework now, but before I do, I would like to point out that optimization functions are the sexiest things ever and I want a job where I can use them. An "optimization function" is a way of solving a problem of efficiency with math. You quantify trends in whatever it is that you're studying and reduce them to as few variables as possible, then, using calculus, you look for patterns in the interactions of the variables - there are key signs that say "this is the best deal you can get."

Example: "What is the most fish we can catch given the fish population?"

Let's say there are one million fish. A trawler fleet can catch a given number of fish in an hour at a rate that is relative to the overall number of fish and the speed at which the crews can haul in a full net. Fish also reproduce at a given rate. There are a lot of other variables.

Using calculus, you can figure out how many trawler-hours should be allocated or allowed for the maximum number of fish with the least work. You can work this out for this year, or the next ten years, or the next hundred. Instead of catching all the fish this year, or catching none, you can strike an exact balance that will not only preserve the fish population, but make sure that you can net a catch of the same size next year, and the year after that and so on, both maximizing profit and preserving the environment - no wait - proving that you can maximize profit by preserving the environment.

You can use this with health care dollars, or your own work-habits.

Math: It's hot stuff.