I want to find the value of $x'$ such that all of the following constraints are satisfied:
$x' * o' < x * o$
$ o' < o $
$ x \le x'$
These are all variables but I always know the values of $x$, $o$ and $o'$. I'm sure that this is easy to solve but I have been completely unable to!
For clarification, what I'm actually trying to do is place two bets on a betting exchange such that I make a profit regardless of the outcome of an event.
I place a back bet of £x at odds of $back_odds$, if that wins then my payout is $£x*back_odds$, I have to place a lay bet at lower odds but with a higher stake in order to make a profit on all outcomes.