This paper proposes an evolutionary technique for the solution of a real - life industrial problem and particular for the product mix selection problem. The evolutionary technique is a combination of a genetic algorithm that preserves the feasibility of the trial solutions with penalties and some local optimization method. The goal of this paper has been achieved in finding the best near optimal solution for the profit fitness function respect to vagueness factor and level of satisfaction. The findings of the profit values will be very useful for the decision makers in the industrial engineering sector for the implementation purpose. It's possible to improve the solutions obtained in this study by employing other meta-heuristic methods such as simulated annealing, tabu Search, ant colony optimization, particle swarm optimization and artificial immune systems. © 2009 American Institute of Physics.