Summary: The extensive use of cloud services in different domains triggers the efficient use of cloud resources to achieve maximum profit. The heterogeneous nature of data centers and the heterogeneous resource requirement of user applications create a scope of improvement in task scheduling. The resource requirements in terms of task constraints must be fulfilled for the tasks to be admitted to the system. Once a task admitted to the system, it may violate service level agreement and incurs penalty due to the disproportionate resource allocation at run time. The latency-sensitive and short-lived workloads need effective scheduling to gain more profit. In this work, we propose Heuristic of Ordering and Mapping for Constraint Aware Profit Maximization (HOM-CAPM) problem for efficient scheduling of tasks with constraints and deadlines to gain maximum profit. The HOM-CAPM approach considers estimation of task execution time in a heterogeneous environment, efficient task ordering, and profit-based task allocation to maximize the overall profit of the cloud system. To gain maximum profit the proposed heuristic considers two cases, (a) not allowing the tasks for execution if it expected to miss its deadline and (b) allowing the task which earns substantial profit even though it is expected to miss its deadline. The results of the extensive simulation using Google trace data as input show that our proposed HOM-CAPM approach generates more profit than other state-of-the-art approaches.