This paper outlines, first, a real-world industrial problem for product-mix selection involving 8 variables and 21 constraints with fuzzy coefficients and thereafter, a multi-objective optimization approach to solve the problem. This problem occurs in production planning in which a decision-maker plays a pivotal role in making decision under fuzzy environment. Decision-maker should be aware of his/her level-of-satisfaction as well as degree of fuzziness while making the product-mix decision. Thus, the authors have analyzed using a modified S-curve membership function the fuzziness patterns and fuzzy sensitivity of the solution found from the multi-objective optimization methodology. An ad hoc Pareto-based multi-objective evolutionary algorithm is proposed to capture multiple non dominated solutions in a single run of the algorithm. Results obtained have been compared with the well-known multi-objective evolutionary algorithm NSGA-II.