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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!

Cheers,

Pete

EDIT:

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.

  • 0
    Are $x'$ and $x$ related in some way, and $o$ and $o'$, too? If so, please describe. If not, please use four different characters (and not $o$). What range of variables are allowable? Is it $\mathbb{R}?2011-03-20

1 Answers 1

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I'll assume that $x$, $o$, and o' are all positive; you should be able to work out solutions in other cases by a similar method.

In this case, we need x \le x' < x(o/o') as our sole requirement, which can be determined by dividing the first expression by o'.

Keep in mind for the other cases that when multiplying/dividing by negative numbers, inequalities are reversed.