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The edge-cloud computing continuum effectively uses fog and cloud servers to meet the quality of service (QoS) requirements of tasks when edge devices cannot meet those requirements. This paper focuses on the workflow offloading problem in edge-cloud computing and formulates this problem as a nonlinear mathematical programming model. The objective function is to minimize the monetary cost of executing a workflow while satisfying constraints related to data dependency among tasks and QoS requirements, including security and deadlines. Additionally, it presents a genetic algorithm for the workflow offloading problem to find near-optimal solutions with the cost minimization objective. The performance of the proposed mathematical model and genetic algorithm is evaluated on several real-world workflows. Experimental results demonstrate that the proposed genetic algorithm can find admissible solutions comparable to the mathematical model and outperforms particle swarm optimization, bee life algorithm, and a hybrid heuristic-genetic algorithm in terms of workflow execution costs.