Determination of the optimal insulation thickness is of great relevance in many thermal engineering applications. In this paper, a simple optimization strategy based on the Lagrange multipliers is presented. The optimal set of thicknesses is analytically found for different constraints and objective functions of interest for the refrigeration industry. Namely, the minimization of heat losses in a single compartment with fixed internal and external volumes and the optimal configuration for a prescribed energy efficiency index. Then, these two basic problems are extended for configurations with two compartments, e.g. domestic refrigerators-freezers, and for configurations with vacuum insulation panels. Optimization problems for realistic configurations show the great potential of the proposed methodology for industrial refrigeration applications.