The delivery of live video channels for services such as twitch.tv leverages the so-called Telco-CDN-Content Delivery Network (CDN) deployed within the Internet Service Provider (ISP) domain. A Telco-CDN can be regarded as an intra-domain overlay network with tight resources and critical deployment constraints. This paper addresses two problems in this context: (1) the construction of the overlays used to deliver the video channels from the entrypoints of the Telco-CDN to the appropriate edge servers; and (2) the allocation of the required resources to these overlays. Since bandwidth is critical for entrypoints and edge servers, our ultimate goal is to deliver as many video channels as possible while minimizing the total bandwidth consumption. To achieve this goal, we propose two approaches: a two-step optimization where the optimal overlays are firstly computed, then an optimal resource allocation based on these pre-computed overlays is performed; and a joint optimization where both optimization problems are simultaneously solved. We also devise fast heuristic algorithms for each of these approaches. The conducted evaluations of these two approaches and algorithms provide useful in- sights into the management of critical Telco-CDN infrastructures.