The Theory of Constraints is a crucial management discipline that argues there is at least one limited resource in each production system, and a solution should be found to overcome this limited resource in order to increase the market share and profitability of firms. As the bottleneck in the system is identified and managed, production will occur on time and be available to the customer, since delays in the production process will be eliminated. Moreover, costs will be reduced as the efficiency at the bottleneck in the production line is improved, and thus the company can reach its profitability targets. The aim of this study is to determine the optimum product mix under the presence of limited resources in the system with the five-step continuous improvement process of the Theory of Constraints. Within this framework, research has been conducted to solve multiple bottleneck problems in a company operating in the metal processing industry. In this application, by analyzing the capacity utilization rates of the resources, the resources at the bottleneck in the system were identified and the optimal product mix was determined. As there is no throughput priority or mathematical method to production of subcomponents in current process, a new algorithm was proposed which is integrating the linear programming and fuzzy logic methodology with the theory of constraints approach. The problem was defined as an integer linear programming model and solved by an optimization software program called GAMS IDE.