Results 1 to 3 of 3

Math Help - LP problem

  1. #1
    Member
    Joined
    Jun 2008
    Posts
    170

    LP problem

    A man deals with French currency (the franc) and American currency (the dollar). At  12 midnight, he can buy francs by paying  .25 dollars per franc and dollars by paying  3 francs per dollar. Let  x_{1} = \text{number of dollars bought (by paying francs)} and  x_{2} = \text{number of francs bought (by paying dollars)} . Assume that both types of transactions take place simultaneously, and the only constraint it that at  12:01 \ \text{A.M.} the man must have a nonnegative number of francs and dollars.

    (a) Formulate an LP that enables the man to maximize the number of dollars he has after all transactions are completed.

    Let  X_{1} = x_{1}+ x_{1}' where  x_{1}' is the number of dollars the man has before the transaction. Similarly, let  X_{2} = x_{2} + x_{2}' where  x_{2}' is the number of francs the man has before the transaction. So is this the correct LP formulation:

    maximize  X_{1} subject to constraints that  X_{1} \geq 0, \ X_{2} \geq 0 . We can solve this right? This formulation allows for the man to not enter any transaction, right?
    Last edited by particlejohn; September 4th 2008 at 08:03 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    I'm not familiar with linear programming, but here is what I'd say: X_1=x'_1+x_1-\frac{x_2}{3} (since \frac{x_2}{3} is the number of dollars spent to buy francs) and X_2=x'_2+x_2-\frac{x_1}{0.25}. Maximize X_1 subject to the constraints X_1\geq0,\ X_2\geq 0.

    (By the way, euros would be more up-to-date than francs)

    Laurent.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2008
    Posts
    170
    Thats all there is too it right? No ambiguities?
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum