Question

Optimization problem...
http://postimg.org/image/adms8rvxj/

(a) is quite straightforward.
(b) is somehow connected to w*d*h=1 and differentiating the formula from (a).

Help with (b)?

Answer 1

b

Answer 2

?

Answer 3

for part b, lets determine everything over w.
we want w*d*h=1
if d=2w so \[2w^2 *h=1\]
then \[h=1/2w^2\]
in equation of M we dont need density or thickness lets get rid them and get
\[2(4w^2+3/2w)=M\]
take differential and find min by equiting value zero
\[16w-3/w^2=0\]
w=3/16 now d and h can be found easily, thnx :)

Answer 4

It's a bit wrong at the end, but you showed me the way (for which i'm thankful). I don't know how i didn't think of this.