Re: [Help-glpk] fraction with vars

[Michael Hennebry]

Divisiblilty can be used to reduce the problem somewhat.

On Fri, 27 Apr 2012, Michael Hennebry wrote:

> # Solve
> # x = p * y / w
> # w * pd * x = pn * y
> # where x, y, w are natural numbers and
> # p = 11 / 17
> # pn = 11
> # pd = 17
> # x in [23, 100]
> # y in [10, 200]
> # w in [3, 7]

# Since pn/pd is in lowest terms, y must be a multiple of pd.

> param w_min := 3;
> param w_max := 7;
>
> param pn := 11;
> param pd := 17;
>
> set I := {w_min..w_max};
>
> var w{I}, binary;
> var y, integer, >= 10, <= 200;
> var x, integer, >= 23, <= 100;

var ypd, integer, >= 10/pd, <= 200/pd
#                     1         11
s.t. y_formula :
    y = ypd*pd;

> s.t. lb{i in I} :
>    i * pd * x >= pn * y - (1-w[i]) * (pn*200-i*pd*23);
     i   *    x >= pn*ypd - (1-w[i]) * (pn*11 -i*   23);

> s.t. ub{i in I} :
>    i * pd * x <= pn * y + (1-w[i]) * (i*pd*100-pn*10);
     i   *    x <= pn*ypd + (1-w[i]) * (i *  100-pn   );

> s.t. sm :
>    sum{i in I} w[i] = 1;
>
> solve;
>
> printf "x = %f\ny = %f\nw = %f\n", x, y, sum{i in I} w[i] * i;
>
> end;

--
Michael   address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword."  --  Lily