sum 100 from given values and limits

Hi all, I'd like to find values that sum 100 between these 4 values and their limits:

low     high   
31.5  33.4
15.3  16.8
47.2  49.1
3.0  3.7

For example a solution could be:

32.0
15.3
49.0
3.7
-------
100

Please help me ;)

Cristiano.

[Matt Kindig]

There are an infinite number of solutions to this problem. Do you just need one that works (i.e., a feasible solution)?

Answer 1

[Roger Stafford]

I propose the following unique "canonical" solution. Let 'low' and 'high' be vectors of your lower and upper range limits respectively and let s be the desired sum.

 t = (s-sum(low))/(sum(high)-sum(low));
 if t<0|t>1
  error('No solution is possible')
 else
  v = low+t*(high-low);
 end

If a solution is possible, elements of the vector 'v' will lie in the proper range and sum to the value s (except for very small round-off errors, of course.)

[Cristiano df]

Thanks all for replies! I would not be able to find a solution without your help.

Many many thanks

Cristiano.

Answer 2

[Image Analyst]

Do you have an array that you're checking to see if its elements are in any one of those 4 ranges? Probably none of them will sum exactly to 100. See the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F YOu can either go greater than 100 or within some tolerance of 100 like the FAQ shows.