We extend to the realm of complex fluids and finite durations the classical problem of extremum work delivered from (or consumed by) the nonequilibrium system composed of a complex fluid, a perfect thermal machine and the environment or an infinite reservoir. The fluid constitutes a valuable resource of a finite how or amount "a finite resource", and work production (consumption) takes place sequentially, in stages of "endoreversible" thermal machines. At each stage, heat and mass transfer takes place in boundary layers which play the role of resistances in the system model. For the fluid at flow, total specific work is extremized at constraints which take into account dynamics of heat and mass transport and rate of work generation. Finite rate limits are obtained for the work production and consumption, which provide stronger bounds that those predicted by classical thermodynamics. Optimal work functions, which incorporate an inevitable minimum of the entropy production are found as functions of end states, duration and (in discrete processes) number of stages. Formal analogies between the entropy production expressions for work-assisted and conventional mass transfer operations help formulate optimization models.