Abstarct: Today, with the increasing expansion of the internet and the growing number of users in areas such as the Internet of Things and cloud computing, a new and emerging field in computer science called Edge Computing has become very important. Edge network technologies aim to bring computational resources closer to users, with the goal of speeding up the computing process by bringing computational servers closer to users and clients. Due to the increasing volume of internet data, bandwidth limitations, constraints on cloud server resources, energy efficiency, and the long distance between cloud servers and users, cloud computing has faced challenges. Edge computing is a step towards addressing these challenges. Users and clients in these networks can offload some of their computations to edge or cloud servers, a process known as offloading. Many networks and systems, including IoT networks, 5G cellular networks, content distribution networks (CDN), autonomous vehicles, smart cities, smart grid energy networks, augmented reality (AR) and virtual reality (VR) applications, healthcare monitoring systems, telemedicine, video streaming and processing systems, and smart traffic management systems, directly benefit from edge computing technology. Therefore, in recent years, edge computing has received significant attention. One of the fundamental topics in the field of edge computing is the optimal resource management problem, which is considered one of the most important challenges in this area. Computational systems with edge network servers and cloud servers seek to respond to user requests using edge network resources as much as possible, preventing them from being sent to the cloud space in order to optimize and expedite the process. Our goal is to present an approach baxsed on the knapsack algorithm to model the resource allocation problem in a network consisting of edge servers and cloud servers and solve it within a reasonable time. The knapsack problem is a well-known problem in combinatorial optimization. A specific type of this problem, called the Multiple Knapsack Problem (MKP), examines which set of items can be selected for each knapsack with limited capacities to maximize the overall value. The multiple knapsack problem is classified as an NP-Hard problem, making solving it within a reasonable time and with limited resources particularly challenging. In our work, assuming that there are knapsacks in both the existing edge servers and cloud servers, and that user tasks to be offloaded onto available resources at the edge or in the cloud are our items, each with its own weight and value, we model and solve the problem. For this purpose, we propose an algorithm that can solve the MKP problem in the mentioned scenario in minimum time and with minimal resources. Our proposed algorithm consists of two parts: the first part calculates the exact solution to the problem when the number of resources and tasks is not large, and the second part finds an approximate solution to the problem using a greedy solution when the number of resources and tasks is very large, making it impossible to calculate it within a reasonable time. After presenting and modeling the problem and proposing our algorithm theoretically, we test our algorithm in practice using the ECHOES simulator designed for testing optimization methods in environments consisting of both cloud and edge. We also discuss and introduce this simulator in detail at the end.