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Linear programming

  1. Dec 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Eva, senior analyst, is determining the optimal investment policy for her reality company, 4-Closure Associative. She has a budget of $6 million for year 1 and $5 million for year 2, and each project can be undertaken as a fraction, up to 100%. Her investment possibilities, in thousands, include, if invested 100%:

    project; investment in year 1; investment in year 2; Return end of year 2
    Rauncho; 1400; 1000; 3100
    Mondo; 200; 70; 450
    Wriggly; 2800; 1600; 5300
    Glory; 900; 500; 2100
    Upson; 1100; 700; 2400

    (i hope it looks clear, it would look clear if you draw a table)
    Funds not invested can be put into a money market account paying 11%.
    Eva wants to maximise hers funds at the end of year 2.
    Formulate a return-maximising Linear program for eva

    2. Relevant equations



    3. The attempt at a solution

    decision variables:
    let x1 be the investment in project Rauncho
    x2 be the investment in project Mondo
    etc...
    x5 be the investment in project Upson

    Maximising so:
    (MAX) f = 3100x1 + 450x2 + 5300x3 + 2100x4 + 2400x5

    subject to the constraints:

    1400x1 + 200x2 + 2800x3 + 900x4 + 1100x5 <= 6000000
    1000x1 + 70x2 + 1600x3 + 500x4 + 700x5 <= 5000000

    Is that correct?
    and also i dont know what to do about the part in the question that says:
    'each project can be undertaken as a fraction, up to 100%'
    and
    'Funds not invested can be put into a money market account paying 11%.'

    Thank you very much.
     
  2. jcsd
  3. Jan 8, 2009 #2
    It's not very important to know what i should do with the part where it says:
    'each project can be undertaken as a fraction, up to 100%'
    but i really have to know what i ahould do with:
    'Funds not invested can be put into a money market account paying 11%.'

    i was thinking about it and maybe i have to inclue a new variable in my constraints to be the money not invested but i still dont know how to do this sincei dont know what will be the coefficient of this new variable; i mean will it be 11% of 5 million and 6 million ???

    Any help or ideas would be very much appreciated.
    Thank you
     
  4. Jan 23, 2009 #3
    I have been working on it and i figured out that we should add a new variable, say x6, where x6 is the money that has not been invested each year.

    so this changes the objective function. Im not 100% sure if this is correct but i think the objective function will be something like this:
    (MAX) f = 3100x1 + 450x2 + 5300x3 + 2100x4 + 2400x5 + x6(1.11)^2
    (i put 1.11 because of the 11% and i put squared because we have two years)
    the first constraint will be:
    1400x1 + 200x2 + 2800x3 + 900x4 + 1100x5 +x6 = 6000
    (since any money left over is x6 and so the total will equal to the total)

    but im not 100% sure how to do the second constraint because we also have to add the money that is left from year one.

    Any ideas??? please. Thank you.
     
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