O15-C917
> restart:
> ps:=(n,x,y)->sum(x['k']*y['k'],'k'=1..n);

                                     n
                                   -----
                                    \
               ps := (n, x, y) ->    )    x['k'] y['k']
                                    /
                                   -----
                                  'k' = 1

> mini:=proc(x,y,n)
> local u,sys;
> u:=[1$n];
> sys:={a*ps(n,x,x)+b*ps(n,u,x)=ps(n,x,y),a*ps(n,x,u)+b*ps(n,u,u)=ps(n,u,y)};
> solve(sys);
> end;

  mini := proc(x, y, n)
local u, sys;
    u := [1 $ n];
    sys := {a*ps(n, x, x) + b*ps(n, u, x) = ps(n, x, y),
        a*ps(n, x, u) + b*ps(n, u, u) = ps(n, u, y)};
    solve(sys)
end

> x:=[1,2,5,7,9]:y:=[1,3,4,7,10]:n:=5:s:=mini(x,y,n);

                                           115
                       s := {b = 1/14, a = ---}
                                           112

> d1:=plot([seq([x[k],y[k]],k=1..n)],style=point,color=black):
> f:=subs(s,a*t+b);

                               115
                          f := --- t + 1/14
                               112

> d2:=plot(f,t=0..10,color=red):
> s1:=mini(y,x,n);

                                  23
                       s1 := {a = --, b = 1/5}
                                  25

> f1:=subs(s1,a*t+b):d3:=plot([f1,t,t=0..10],color=blue):
> with(plots):display([d1,d2,d3]);

>