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Math Help - Decision making problem

  1. #1
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    Question Decision making problem

    Hi Guys,

    I've got this problem where I need to select a carton of milk, 2 bottles of water and a juice box out of a list shown below. The idea is to select the 4 items that will allow me to end up with the largest possible total Litres. However the trick is that it must be done as if there were 3 other people trying to do the same thing and we each take it in turns. Eg. If I select the 2L of milk first, the other 3 people would then each select something else.

    Milk: 2L, 1.5L, 1.25L, 1L
    Water: 3L, 2.75L, 2.5L, 2.25L, 2L, 1.5L, 1L, 500mL
    Juice Box: 700mL, 500mL, 400mL, 250mL

    I thought about working out the average for each type and selecting the container with the largest different between what's available and the average but that's really just a guess.

    Any help would be greatly appreciated!
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  2. #2
    MHF Contributor

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    Re: Decision making problem

    Sounds to me like you need to use the "greedy algorithm" which is just a fancy way of saying that each time you have a choice, you take the best remaining. Here, you just want to get "largest possible total Litres" without regard to what is in the container. Assuming you get to go first, you should take the 3 L water bottle. The other three people, assuming they are following the the same "algorithm", will choose 2.75 L, 2.5 L, and 2.25 L water bottles. That leaves the 2L milk and 2L water bottles for you. Take either one of them. The other three people will take the other 2 L bottle, and the two 1.5 L bottles. Continue always taking the largest remaining bottle.

    (If the other three people do NOT follow this algorithm, you still take the largest bottle remaining. You will just do better than if they followed the "greedy algorithm" also.)
    Last edited by HallsofIvy; February 27th 2013 at 07:02 AM.
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  3. #3
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    Re: Decision making problem

    Thanks HallofIvy, but the thing about this problem is that I don't need to give the answer, I need to give the method to how I would approach this answer in any case. The numbers I provided aren't accurate because I don't have the problem with me, but they are there to give a better idea of the problem. I think the main mistake I made in the numbers provided was that the first juice box should've been around 1.5L, providing a big gap between that and the next lot. I was told the answer is not as simple as taking the container with the largest number of litres each time.
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  4. #4
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    Re: Decision making problem

    shall I post this somewhere else? Really need an answer
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