This paper considers the problem of service placement and task scheduling on a three-tiered edge-to-cloud platform when user requests must be met by a certain deadline. Time-sensitive applications (e.g., augmented reality, gaming, real-time video analysis) have tight constraints that must be met. With multiple possible computation centers, the "where" and "when" of solving these requests becomes paramount when meeting their deadlines. We formulate the problem of meeting users' deadlines while minimizing the total cost of the edge-to-cloud service provider as an Integer Linear Programming (ILP) problem. We show the NP-hardness of this problem, and propose two heuristics based on making decisions on a local vs global scale. We vary the number of users, the QoS constraint, and the cost difference between remote cloud and cloudlets(edge clouds), and run multiple Monte-Carlo runs for each case. Our simulation results show that the proposed heuristics are performing close to optimal while reducing the complexity.