The Geek Forum
Main Forums => Anarchy => Topic started by: Jaepheth on January 28, 2011, 10:23:56 PM
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It seems to be the cool thing to do, so here you go:
Adam buys one kilogram of sugar every Monday.
Bob buys one dollar's worth of sugar every Wednesday.
The price of sugar may change on Sundays only.
Who gets the best deal over time? Justify your answer.
Monte Carlo solutions will not be accepted.
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It seems to be the cool thing to do, so here your go:
Adam buys one kilogram of sugar every Monday.
Bob buys one dollar's worth of sugar every Wednesday.
The price of sugar may change on Sundays only.
Who gets the best deal over time? Justify your answer.
Monte Carlo solutions will not be accepted.
Insufficient data.
But, assuming that the sugar is priced per pound, and Adam and Bob are both using dollars, then Adam and Bob are both paying the same price for the sugar, and purchasing the same amount of sugar per dollar. So neither has an advantage, unless you postulate that the sugar at the top of the barrel is qualitatively different from the sugar deeper down in the barrel (provided the sugar is in fact stored in barrels), in which case either Adam or Bob gets the best deal over time, depending on whether the sugar at the top is better or worse than the sugar deeper down, and provided that a new barrel is cracked open on Sunday or Monday morning, or some time Tuesday or Wednesday morning, which is totally not determined. Provided also that we're looking at a sufficiently long period of time, so that the fluctuations of the dollar versus the value of sugar as a commodity is evened out.
What's a Monte Carlo solution?
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Insufficient data.
But, assuming that the sugar is priced per pound, and Adam and Bob are both using dollars, then Adam and Bob are both paying the same price for the sugar, and purchasing the same amount of sugar per dollar. So neither has an advantage, unless you postulate that the sugar at the top of the barrel is qualitatively different from the sugar deeper down in the barrel (provided the sugar is in fact stored in barrels), in which case either Adam or Bob gets the best deal over time, depending on whether the sugar at the top is better or worse than the sugar deeper down, and provided that a new barrel is cracked open on Sunday or Monday morning, or some time Tuesday or Wednesday morning, which is totally not determined. Provided also that we're looking at a sufficiently long period of time, so that the fluctuations of the dollar versus the value of sugar as a commodity is evened out.
What's a Monte Carlo solution?
A Monte Carlo (http://en.wikipedia.org/wiki/Monte_carlo_method) solution would be generating random prices and calculating who gets the best Dollar to pounds of sugar ratio.
You can use it to find the right answer, you just can't use it as a proof.
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Ok, since this is a pretty difficult problem I'll give you all a Big Hint (http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality)
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Ok, I'm going to try to work on this in the next few days.