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Math Help - Stunned by my finite mathematics question

  1. #1
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    Talking Stunned by my finite mathematics question

    Im studying finite maths right now, and i came across this question which is rather difficult...i would like some help in solving this question

    A manufacturer has three divisions, which produce electricity, steel and petrol. To produce $1 of electricity, the division needs $0.02 worth of electricity, $0.20 worth of steel and $0.10 worth of petrol. To produce $1 of steel, the division needs $0.02 worth of electricity, $0.01 worth of steel and $0.02 worth of petrol. To produce $1 of petrol, the division needs $0.10 worth of electricity, $0.01 worth of petrol. The manufacturer estimates the sales demand to be $300 million for the electricity division, $100 million for the steel division and $200 million for the petrol division. At what level should each division produce in order to satisfy this demand?

    thanks in advanced =D
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  2. #2
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    Re: Stunned by my finite mathematics question

    Are you studying Linear Programming? Let's see you set it up.
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  3. #3
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    Re: Stunned by my finite mathematics question

    There may be an alternative in old fashioned simultaneous equations:


    Define:
    e = electricity produced ($m)
    s = petrol produced ($m)
    s = petrol produced ($m).

    The production of each must satisfy the external market demand and also the demand from the other divisions. So for electrcity this would be:

    300 (external)
    0.02e (demand from electric division for electricity)
    0.1p (demand from petrol division for electricity)
    0.02s (demand from steel division for electricity)

    so (and similarly for the other divisions):
    e=300 + 0.02e + 0.1p + 0.02s
    s=100 + 0.2e + 0.01s
    p=200 + 0.1e + 0.02s + 0.01p


    That is 3 equations in 3 unknowns, solve using your preferred method.
    Last edited by SpringFan25; July 5th 2011 at 11:01 AM.
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  4. #4
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    Re: Stunned by my finite mathematics question

    well my lecturer said i could solve it using gauss-jordan elimination method, but when i tried, i got answers with a lot of decimals..which looked wrong

    could you elaborate further please =D

    thanks
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  5. #5
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    Re: Stunned by my finite mathematics question

    It would be better if you showed how you tried to solve those equations.
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  6. #6
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    Re: Stunned by my finite mathematics question

    lets say, electricity = x , steel = y , petrol = z
    then,

    $1 electricity=0.02x + 0.20y + 0.10z

    $1 steel = 0.02x + 0.01y + 0.02z

    $1 petrol = 0.10x + 0.01z

    i multiplied the LHS to meet the demand level, say,
    $1 electricity x 300 mil
    $1 steel x 100mil
    $1 petrol x 200mil

    then,
    300000000 = 6000000x + 60000000y + 30000000
    100000000 = 2000000x + 1000000y + 2000000z
    200000000 = 20000000x + 2000000z

    after that, i solved those equations simultaneously, i get

    x = 550/131
    y = -3200/131
    z = 7600/131

    HELP, im lost
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