If you just factor the original polynomial(The area) then you will find that one of the factors is c-2(the length) and the other will be the width.
When I factored it, I got 2c+3 as the width.
:)
Http://ncert.nic.in/ncerts/l/gemp109.pdf
see if it helps if not I am sorry
If you know that
, then you know right away

###
Otherwise, you can derive the same result. Let
, so that
.
is bounded, so we know
. For these values of
, we always have
.
So, recalling the Pythagorean theorem, we find

Then

as expected.
4/3 x 7=9.3333
4/3 x 8=10.666
Can't go over 10, so you can only make 7 batches.
Hope I've helped!