As　an　emerging　framework,　edge　computing　achieves　Internet　of　Things　by　providing　computing,　storage　and　network　resources.　It　moves　computation　to　edge　devices　located　near　users.　Nevertheless,　nodes　in　the　edge　often　own　limited　resources　and　constrained　energy　capacities.　It　is　impossible　to　entirely　execute　tasks　in　the　edge　due　to　their　unsatisfied　quality　of　service.　Cloud　data　centers　(CDCs)　own　almost　unlimited　resources　yet　they　might　cause　large　transmission　delay　and　high　resource　cost.　Consequently,　it　is　highly　needed　to　intelligently　offload　tasks　between　CDC　and　edge.　This　work　proposes　a　task　offloading　algorithm　for　hybrid　cloud-edge　systems　to　achieve　profit　maximization　of　a　system　provider　with　response　time　bound　assurance.　It　comprehensively　investigates　CPU,　memory　and　bandwidth　limits　of　nodes　in　the　edge,　and　constraints　of　available　energy　and　servers　in　CDC.　These　factors　are　integrated　into　a　single-objective　constrained　optimization　problem,　which　is　solved　by　a　simulated-annealing-based　migrating　birds　optimization　algorithm　to　yield　a　close-to-optimal　offloading　policy　between　CDC　and　the　edge.　Real-life　data-driven　experimental　results　show　that　its　profit　outperforms　its　four　typical　peers.　©　2020　IEEE.