Growing remote health system allows continuous monitoring of patients' conditions outside medical facilities. However, the real-time smart-healthcare applications having latency limitations, must be solved efficiently. Fog computing is emerging as an efficient solution for such real-time applications. Therefore, Medical Centers (MCs) are becoming more interested in offering IoT-based remote health monitoring services to get profited by deploying fog resources. However, an efficient algorithmic model for allocating limited fog computing resources in a criticality-aware smart-healthcare system while considering the profit of MCs is needed. Thus, we formulate an optimization problem by maximizing system utility, calculate as a linear combination of MC's profit and patients' cost together. We propose a flat-pricing based scheme to measure the profit of MC in health monitoring system. Further, we propose a swapping-based heuristic to maximize the system utility. The proposed heuristic is evaluated on various parameters and shown to be closed to the optimal while considering the criticality of patients and the profit of MC, together. Through extensive simulations, analysis on real-world data and prototype implementation, we find that the proposed heuristic achieves an average utility of 94.5% of the optimal, in polynomial time complexity.