Yarn tenacity is one of the most important properties in yarn production. This paper addresses modeling of yarn tenacity as well as optimally determining the amounts of the effective inputs to produce yarn with desired tenacity. The artificial neural network is used as a suitable structure for tenacity modeling of cotton yarn with 30 Ne. As the first step for modeling, the empirical data is collected for cotton yarns. Then, the structure of the neural network is determined and its parameters are adjusted by back propagation method. The efficiency and accuracy of the neural model is measured based on percentage of error as well as coefficient determination. The obtained experimental results show that the neural model could predicate the tenacity with less than 3.5% error. Afterwards, utilizing genetic algorithms, a new method is proposed for optimal determination of input values in yarn production to reach the desired tenacity. We conducted several experiments for different ranges with various production cost functions. The proposed approach could find the best input values to reach the desired tenacity considering the production costs.