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Math Help - Linear Programming: Shares and Dividends

  1. #1
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    Linear Programming: Shares and Dividends

    Hi all,

    I have two eqns which are related to stock and dividends which i think LP could help to solve( .. i hope).

    5.5x + 2.5y = theta
    67.00x + 28y = 200 000
    x>0, y>0, theta>0

    I derived the above two eqns from this:
    Stock A is @ 67.00
    Stock B is @ 28.00

    Stock A pays 5.5 dollars per share annually
    Stock B pays 2.5 dollars per share annually.
    (ie. if i get 1 x 67.00 and 0 x 28.00, that year i'll get $5.50)

    My question is how to derive the set of {x,y} that would yield a max theta?


    Million thanks,
    Gary
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  2. #2
    A riddle wrapped in an enigma
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    Big Stone Gap, Virginia
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    Quote Originally Posted by glaboratory View Post
    Hi all,

    I have two eqns which are related to stock and dividends which i think LP could help to solve( .. i hope).

    5.5x + 2.5y = theta ====> "I assume this is your profit function"
    67.00x + 28y = 200 000 ====> "I don't understand where this came from"
    x>0, y>0, theta>0

    I derived the above two eqns from this:
    Stock A is @ 67.00
    Stock B is @ 28.00

    Stock A pays 5.5 dollars per share annually
    Stock B pays 2.5 dollars per share annually.
    (ie. if i get 1 x 67.00 and 0 x 28.00, that year i'll get $5.50)

    My question is how to derive the set of {x,y} that would yield a max theta?


    Million thanks,
    Gary
    Hi Gary,

    My guess is that the above equation in red should be an inequality to represent some kind of restraint, but there's not enough info to determine what that restraint is.

    Do you just have $200,000 to invest? If so, the restraint would be:

    67x+28y \leq 200000

    But, even with these constraints, we end up with an unbounded region. So, we need more detail.
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  3. #3
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    Mar 2009
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    Hi masters

    Yes, i have 200000 to invest and yes your constraint is correct

    if i am correct, i think the unbounded region is the theta.

    i think i am not sure how to estimate theta such that x and y are bounded.

    Million thanks,
    Gary
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