A sustainable city requires a sustainable means of transportation. This ambition is leading towards a higher penetration of electric vehicles (EVs) in our cities, in both the private and commercial sectors, putting more and more burden on the existing power grid. Modern deregulated power grids vary electricity tariffs from location to location and from time to time, to compensate for any additional burden. In this paper, we propose a profit-aware solution to strategically manage the movements of EVs in the city to support the grid while exploiting these locational, time-varying prices. This work is divided into three parts: M1) Profit-aware charging location and optimal route selection, M2) Profit-aware charging & discharging location and optimal route selection, and M2b) Profit-aware charging & discharging location and optimal route selection considering the demand-side flexibility. This work is tested on the MATLAB programming platform using the Gurobi optimisation solver. From the extensive case study, it is found that M1 can yield profits up to 2 times more than those of its competitors, whereas M2 can achieve profits up to 2.5 times higher and simultaneously provide substantial grid support. Additionally, M2b extension has made M2 more efficient in terms of grid support.