Suppose that we have a set of items and a set of devices, each possessing
two limited resources. Each item requires a given amount of the resources.
Further, each item is associated with a profit and
a color, and items of the same color can {\em share} the use of
one resource.
We need to allocate the resources to the most profitable (feasible)
subset of items.
In alternative formulation, we need to {\em pack} the most profitable subset
of items in a set of $2$-dimensional bins (knapsacks),
in which the capacity in one dimension is {\em sharable}.
Indeed, the special case where we have a single item in each color
is the well-known {\em $2$-dimensional vector packing ($2$DVP)} problem.
Thus, the problem that we study is strongly NP-hard
for a single bin, and MAX-SNP hard for multiple bins.
Our problem has several important applications, including
{\em data placement} on disks in media-on-demand systems.
We present approximation algorithms as well as optimal
solutions for some instances. In some cases, our results are similar to the
best known results for $2$DVP. Specifically, for a single knapsack,
we show that our problem is solvable in pseudo-polynomial time
and develop a {\em polynomial time approximation scheme (PTAS)}
for general instances.
For a natural subclass of instances we obtain a simpler scheme.
This yields the first {\em combinatorial} PTAS for a
non-trivial subclass of instances for $2$DVP.
For multiple knapsacks, we develop a PTAS for a subclass of instances
arising in the data placement problem.
Finally, we show that when the number of distinct colors in the
instance is fixed, our problem admits a PTAS, even if the items have
arbitrary sizes and profits, and the bins are arbitrary.