# 6.2  The Most Economical Tin Can
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 6.2.
# In-line plots have been removed to conserve disk space.
> restart; s:=2*Pi*r^2 + 2*Pi*r*h;

                                  2
                       s := 2 Pi r  + 2 Pi r h

> l:=4*Pi*r + h;

                           l := 4 Pi r + h

> c:=a*s + b*l; a:=0.01; b:=0.2;

                           2
             c := a (2 Pi r  + 2 Pi r h) + b (4 Pi r + h)


                               a := .01


                               b := .2

> h:=1000 / (Pi*r^2); c;

                                   1000
                              h := -----
                                       2
                                   Pi r


                         2   20.00             200.0
                 .02 Pi r  + ----- + .8 Pi r + -----
                               r                   2
                                               Pi r

> plot(c, r=1..10);
> Dc:=diff(c, r); rbest:=fsolve(Dc=0, r=3..5);

                                 20.00           400.0
                Dc := .04 Pi r - ----- + .8 Pi - -----
                                   2                 3
                                  r              Pi r


                         rbest := 4.104217144

> evalf(subs(r=rbest, h));

                             18.89685223

>