In this work, a robust optimization model for business production mix problem is introduced to minimize the production cost. We apply conic programming technique to the original production cost minimization problem and formulate the model in the form of second-order cone programming (SOCP) problem which is an emerging branch in current research. For decision taking, optimization plays the crucial role. In robust optimization, we have to optimize a problem where some data are not provided directly but it is declared that the data are contained in a predefined set. Minimizing the production cost for production business is a big interest to maximize the profit. In this research, we propose a robust optimization model for production in business which minimizes the production cost maintaining the quality of product. To formulate the propose model, we use conic programming technique considering the worst-case in the ratio of ingredients in product materials and introduce the model in the form of second-order cone programming (SOCP) problem. So far we studied, this is the first time application of conic programming in minimization of production cost problems. The proposed robust model is presented as an alternative option to minimize the production cost maintaining the quality of product rather than the optimal value of the problem. Of course, the proposed model can minimize the production cost compared to the original problem since it is more robust.