Formula Student Driverless (FSD) is a competition where student teams compete to build an autonomous racecar. The main dynamic event in FSD is trackdrive, where the racecar traverses an unknown track with lanes demarcated by cones. One major challenge of the event is to determine the boundaries of the lane from cones perceived online despite false positive cone detections and sharp turns. We present a binary integer optimization to address this problem by leveraging a priori knowledge from competition rules on parameters such as average cone spacings and minimum track width. In this paper, we describe our approach, and analyze its latency, accuracy, and robustness to false positive cone detections. This approach is used on-board to solve the lane detection problem during the competition in real-time.