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Math Help - Linear Equations and Matrices

  1. #1
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    Linear Equations and Matrices

    A simple economy is based on 3 commodities: grain, fuel and transportation.
    Production of 1 unit of grain requires 1/4 unit of fuel and 1/3 unit of transportation
    Production of 1 unit of fuel requires 1/2 unit of grain and 1/4 unit of transportation,
    Production of 1 unit of transportation requires 1/4 unit of grain and 1/4 unit of fuel.
    Find the input-output matrix for this situation and the gross output required for a net production of 516 units of grain, 258 units of fuel and 129 units of transportation.
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  2. #2
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    Quote Originally Posted by vuze88 View Post
    A simple economy is based on 3 commodities: grain, fuel and transportation.
    Production of 1 unit of grain requires 1/4 unit of fuel and 1/3 unit of transportation
    Production of 1 unit of fuel requires 1/2 unit of grain and 1/4 unit of transportation,
    Production of 1 unit of transportation requires 1/4 unit of grain and 1/4 unit of fuel.
    Find the input-output matrix for this situation and the gross output required for a net production of 516 units of grain, 258 units of fuel and 129 units of transportation.
    G F T
    G 1 1/4 1/3 | x | |561|
    F 1/2 1 1/4 | y | = |258|
    T 1/4 1/4 1 | z | |129|
    It is in the form of A*X = P
    SO X = A^-1*P
    Last edited by sa-ri-ga-ma; March 3rd 2010 at 04:30 PM.
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