We consider the problem proposed by Thales Nederland at the SWI 2012 meeting. Thales Nederland is the Dutch branch of the international Thales Group. The company specializes in designing and producing professional electronics for defence and security applications, such as radar and communication systems. Moreover, Thales Nederland acts as a local point of contact for the complete portfolio of the Thales Group. During the SWI 2012 meeting, on behalf of Thales Nederland, Dr. Maurits de Graaf posed several questions regarding the maximization of the lifetime of a wireless sensor network. We addressed these questions during the workshop and our most significant results are summarized as follows: We have proven that this lifetime maximization problem, even under the most simple constraints, is NPcomplete, so it is not possible to find an algorithm that gives the optimal solution within polynomial time. Furthermore, we have constructed a counterexample to illustrate that the heuristic currently used by Thales can be asymptotically at least logn times worse than the optimal solution. Moreover, we have developed a new heuristic and have illustrated with several numerical examples that it performs better than the heuristic currently used by Thales. Finally, we have formulated the problem as a linear programming problem and used this to quantify how far the heuristic used by Thales is from being optimal.