The Lead-Based Multiple Video Transmission (LMVT) problem is motivated by applications in managing the quality of experience (QoE) of video streaming for mobile clients. In an earlier work, the LMVT problem has been shown to be NP-hard for a specific bit-to-lead conversion function $φ$. In this work, we show the problem to be NP-hard even if the function $φ$ is linear. We then design a fully polynomial time approximation scheme (FPTAS) for the problem. This problem is exactly equivalent to the Santa Clause Problem on which there has been a lot of work done off-late.