5 more than the sum of p and a
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Not necessarily. 
and 
may be linearly dependent, so that their span forms a subspace of 
that does not contain every vector in .
For example, we could have
and 
. Any vector 
of the form 
, where 
, is impossible to obtain as a linear combination of these and , since
unless
and 
.
For example, we could have
unless
If x represents the length of the box, then 42-x will be the girth. Since the largest area for a given girth is that of a square, the side length of the square cross section is (42 -x)/4.
The volume as a function of package length is then
.. v(x) = x((42-x)/4)^2
This has a maximum at x=14. The corresponding volume is 686 in^3.
The volume as a function of package length is then
.. v(x) = x((42-x)/4)^2
This has a maximum at x=14. The corresponding volume is 686 in^3.