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Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. In this paper, a neutrosophic linear programming (NLP) problem with single-valued trapezoidal neutrosophic numbers is formulated and solved. A new method based on the so-called score function to find the neutrosophic optimal solution of fully neutrosophic linear programming (FNLP) problem is proposed. This method is more flexible than the linear programming (LP) problem, where it allows the decision maker to choose the preference he is willing to take. A stock portfolio problem is introduced as an application. Also, a numerical example is given to illustrate the utility and practically of the method.