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In this paper we consider the following {\em maximum budgeted allocation}(MBA) problem: Given a set of $m$ indivisible items and$n$ agents; each agent $i$ willing to pay $\bij$ on item $j$ and with a maximum budget of $B_i$, the goal is to allocate itemsto agents to maximize revenue.The problem naturally arises as auctioneer revenue maximization in budget-constrained auctions and as winner determinationproblem in combinatorial auctions when utilities of agents are budgeted-additive. Our main results are:- We give a $3/4$-approximation algorithm for MBA improving upon the previous best of $\simeq 0.632$\cite{AM,FV}. Our techniques are based on a natural LP relaxation of MBA and our factor is optimal in the sense that it matches the integrality gap of the LP.- We prove it is NP-hard to approximate MBA to any factor better than $15/16$, previously only NP-hardness was known \cite{SS,LLN}. Our result also implies NP-hardness of approximating maximum submodular welfare with {\em demand oracle} to a factor better than $15/16$, improving upon the best known hardness of $275/276$\cite{FV}.- Our hardness techniques can be modified to prove that it is NP-hard to approximate the {\em Generalized Assignment Problem} (GAP) to any factor better than $10/11$. This improves upon the $422/423$ hardness of \cite{CK,CC}.We use {\em iterative rounding} on a natural LP relaxation of MBA to obtain the $3/4$-approximation. We also give a $(3/4 - \epsilon)$-factoralgorithm based on the primal-dual schema which runs in $\tilde{O}(nm)$ time, for any constant $\epsilon 0$.