Locomotion is widely observed in life at micrometric scales and is exhibited by many eukaryotic unicellular organisms. Motility of such organisms can be achieved through periodic deformations of a tail-like projection called the eukaryotic flagellum. Although the mechanism allowing the flagellum to deform is largely understood, questions related to the functional significance of the observed beating patterns remain unresolved. Here, we focus our attention on the stroke patterns of biflagellated phytoplanktons resembling the green alga Chlamydomonas. Such organisms have been widely observed to beat their flagella in two different ways--a breaststroke and an undulatory stroke--both of which are prototypical of general beating patterns observed in eukaryotes. We develop a general optimization procedure to determine the existence of optimal swimming gaits and investigate their functional significance with respect to locomotion and nutrient uptake. Both the undulatory and the breaststroke represent local optima for efficient swimming. With respect to the generation of feeding currents, we found the breaststroke to be optimal and to enhance nutrient uptake significantly, particularly when the organism is immersed in a gradient of nutrients.