Just a quick math question...

Discussion in 'Off-Topic Discussions' started by Mr. Engineer, Apr 20, 2005.

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  1. Mr. Engineer

    Mr. Engineer member

    I wanted to confirm an equasion and was hoping to receive some feedback from the math guru's in the crowd.

    I am selling 5 type of dogs.

    Dog 4 sales cannot exceed l more than 10% of the total amount of dogs sales 1-3

    Is the equation

    X4 </= .1X1 + .1X2 +.1X3

    which in standard form should be

    .1X1 + .1X2 + .1X4 - X4 </= 0

    Is this the way I would write this mathmatically?

    Thanks!
     
  2. Mike Albrecht

    Mike Albrecht New Member

    You are off by one dog that you can sell

    Dog 4 sales cannot exceed l more than 10% of the total amount of dogs sales 1-3

    Dog4 = X4
    Dog1 = X1
    Dog2 = X2
    Dog3 = X3

    Thus: X4 <= 0.1*(X1 + X2 + X3) +1
    or

    X4 - 0.1*(X1 + X2 + X3) <=1
    X4 - 0.1X1 - 0.1X2 - 0.1X3 <=1
     
  3. JLV

    JLV Active Member

    I am not a guru math, but I am pretty sure you got the sign of that inequality wrong.

    X4 </= .1X1 + .1X2 +.1X3

    That one was correct (in my view), and would solve the problem (also in my view). However whenyou rearrange it, I think you do it wrong

    .1X1 + .1X2 + .1X4 - X4 </= 0

    This is how todo it.

    X4 </= .1X1 + .1X2 +.1X3

    Then you sustract X4 to BOTH sides of the inequality. Thus you get:

    X4 - X4 </= .1X1 + .1X2 +.1X3 - X4

    Reorganizaing again,


    0 </= .1X1 + .1X2 +.1X3 - X4


    Or,


    .1X1 + .1X2 +.1X3 - X4 >/= 0


    That´s your inequality (if I am correct). I don´t understand what Mike did so I may be totally wrong.



    Regards
     
  4. JLV

    JLV Active Member

    Unless you have to sell one and only one dog of type five.
     
  5. Mike Albrecht

    Mike Albrecht New Member

    Back to the problem.

    Dog 4 sales cannot exceed l more than 10% of the total amount of dogs sales 1-3

    Dog4 = X4

    For example, if,

    Dog1 = X1 = 10
    Dog2 = X2 = 10
    Dog3 = X3 = 10

    Then by your formula: X4 </= .1(10) + .1(10) +.1(10) = 3

    or 1 + 1 + 1 - 3 >/= 0, while it is = 0, it is not >= 0

    if you use X4 <= 0.1*(X1 + X2 + X3) +1 then

    X4 <= 0.1*(10+10+10) +1 = 4
    which is 1 more than 10% of the total amount of dogs sales 1-3

    and

    X4 - 0.1*(10 + 10 + 10) <=1

    4 - 3 <= 1

    (BTW: no mention was made in the data of Dog 5, whihc would indicate no constraint on their sales).
     
  6. JLV

    JLV Active Member

    I think this is the part I find confussing, Mike. X4 =0 is a solution (the trivial solution) even for that particular case you mention X1 = X2 = X3 = 10. I mean, 0 is clearly greater than or equal to zero.Thus 0 >=0; so the inequality, even in the specific case you mention, still holds (when X1 = X2 = X3 = 10). Just for the sake of arguing about an interesting subject, I don´t see the necessity to include that ONE in the right part of the inequality. Why? (I have read your explanation 5 times but I still don´t understand WHY?) :confused:

    (I just hope we are not misleading Mr. Engineer who already have enough problems of his own :( )
     
  7. PhD2B

    PhD2B Dazed and Confused

    Since the 5th type of dog has no bearing on this problem, your first equation looks fine.

    The standard form, however, would look like this:

    X4 - .1X1 - .1X2 - .1X3 <= 0
     
  8. JLV

    JLV Active Member

    Yes, I agree with that too, PhD2B.
     
  9. Mike Albrecht

    Mike Albrecht New Member

    One minor point still, the question did not read

    Dog 4 sales cannot exceed 10% of the total amount of dogs sales 1-3


    But rather

    Dog 4 sales cannot exceed l more than 10% of the total amount of dogs sales 1-3

    .1X1 + .1X2 +.1X3 - X4 >/= 0

    Has X4 being 1 less than the correct answer.

    .1X1 + .1X2 +.1X3 - X4 </= 0

    Would be correct as X4 can be equal to or greater than .1X1 + .1X2 +.1X3
     
  10. JLV

    JLV Active Member

    Ok, I read l and not 1. I thought it was a typo after I read the solution Mr. Engineer proposed for this problem. This is then the origin of the discrepancies,and that explains everything.


    Thanks
     
  11. PhD2B

    PhD2B Dazed and Confused

    I also read l as a typo and not as 1.

    Only Mr. Engineer knows for sure... :)
     
  12. Mr. Engineer

    Mr. Engineer member

    I actually went over this problem for 4 additional hours until I got it right. I appreciate all of the great responses. Like I said before, I think I am finally catching on to what is required for this class!
     

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