We present a simple combinatorial 21−e−2-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within factor better than 1−1/e
Nearby in the stack
. We show that the algorithm can be extended to yield a ratio of
k+11−e−(k+1)
for the problem with a single knapsack and the intersection of
k
matroid constraints, for any fixed
k>1
. Our algorithms, which combine the greedy algorithm of [Khuller, Moss and Naor, 1999] and [Sviridenko, 2004] with local search, show the power of this natural framework in submodular maximization with combined constraints.