Chinese Remainder Therom

I know, the name of the post sounds really weird but trust me, its the best I can think of. Today, I was in my math modelling class. What an interesting subject, math modeling. My lecturer was going on about the chinese remainder theorem on how with just one formulae, you can solve any equation, be it 3 different unknowns, 4 different unknowns and so on. What struck me was that one simple careless mistake could make the entire math problem go haywire. That's the one thing i hate about maths. Simple to apply at times, horrible to do at times. Imagine your soccer team being in a yo - yo form. One day playing marvelously, pure attacking football and giving opposing strikers hell at the back. The next match, woeful, trashed 6-0. Rubbish, absolute rubbish. That I feel is probably what maths like. Simplex method ah so nice to use. Its interesting but try doing it with numbers as big as a T-rex. (3 digits and more) You'd probably cry out of frustration and your mind will beg you to stop thinking. Clear minds are always good for maths. Always.

Imagine this question for the Chinese Remainder Theorem

X - 3 (mod4)
X - 4 (mod 5)
X - 7 (mod 3)
X - 2 (mod 7)

How do you solve that? Go figure. And mind you, this is how to decode mesages, well except that the prime numbers are huge, and when i mean huge i really do mean huge. 101 and above!!!


Heres another one for the weary minds. Am I evil or what?

Maximise
5 x + 3y with regards to

2 x + y <= 0
4 x + 6y <= 0
3x + y <= 0
x + 7y <= 0

Haha, signing off.

ps:
The numbers I made them up, not some random book I borrowed from the library or lecture notes.