Re: Find two elements which give a fixed sum

"Edoardo" wrote in message <mpb39b$1kb$1@newscl01ah.mathworks.com>...
> I tried to solve this problem:
>
> find the value of both x1 and x2 in the following expression
>
> c1= a1*x1+a2*x2
>
> where:
>
> c1 is a given value
>
> a1 and a2 are constants
>
> x1 is bounded between 1400 and 1650
>
> x2 is bounded between 95 and 195
>
> I tried to use linear programming optimization with equality constrain but seems to not work.
>
> It seems a really simple problem for me but I am not able to produce a code so solve it
>
> Thanks for your help and time

Trivial. (Sorry, but it is.) Why bother with an LP code even?
linprog will have no problem, but why bother?

You know, for example, that x2 lives in the interval [95,195].

Think in terms of intervals now, and solve for x1.

  c1= a1*x1+a2*[95,195]

So we know that

  x1_interval = (c1 - a2*[95 195])/a1

If a1, c1, a2 are all known constants, then the result will
be a vector of TWO numbers, that bound the possible
values of x1.

For example, I'll pick some numbers here...

  c1 = 3950;
  a2 = 5;
  a1 = 2;
  x1_interval = (c1 - a2*[95 195])/a1

  x1_interval =
       1737.5 1487.5

So ANY number for x1 in that interval will result in a valid
solution for x2.

You said that x1 must lie in the interval [1400, 1650].

So, lets pick the value for x1 now. Any number in that
interval is fine, as long as it is in the limits we must impose.

  x1 = 1500;
  x2 = (c1 - a1*x1)/a2
  x2 =
     190

Nothing complicated was needed at all.

John