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!

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

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

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).

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

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

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

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

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!