  In this note we study packing or covering integer programs with at most k
constraints, which are also known as k-dimensional knapsack problems. For any
integer k > 0 and real epsilon > 0, we observe there is a polynomial-sized LP
for the k-dimensional knapsack problem with integrality gap at most 1+epsilon.
The variables may be unbounded or have arbitrary upper bounds. In the packing
case, we can also remove the dependence of the LP on the cost-function,
yielding a polyhedral approximation of the integer hull. This generalizes a
recent result of Bienstock on the classical knapsack problem.
