The cold startup of the container is regarded as a crucial problem to the performance of serverless computing, especially to the resource-capacitated edge clouds. Pre-warming hot containers has been proved as an efficient solution but is at the expense of high memory consumption. Instead of pre-warming a complete container for a function, recent studies advocate Zygote container, which pre-imports some packages and is able to import the other dependent packages at runtime, so as to avoid the cold startup problem. However, as different functions have different package dependencies, how to plan the Zygote generation and pre-warming in a resource-capacitated edge cloud becomes a critical challenge. In this paper, aiming to minimize the overall function startup time and subjective to the resource capacity constraints, we formulate this problem into a Quadratic Integer Programming (QIP) form. We further propose a Randomized Rounding based Zygote Planning (RRZP) algorithm. The performance efficiency of our algorithm is proved via both theoretical analysis and trace-driven simulations. The results show that our algorithm can significantly reduce the startup time by 25.6%.