A portfolio selection model is derived for diffusions where inequality constraints are imposed on portfolio security weights. Using the method of stochastic dynamic programming Hamilton-Jacobi-Bellman (HJB) equations are obtained for the problem of maximizing the expected utility of terminal wealth over a finite time horizon. Optimal portfolio weights are given in feedback form in terms of the solution of the HJB equations and its partial derivatives. An analysis of the no-constraining (NC) region of a portfolio is also conducted.