{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"b6e3865b-127b-5f16-8b17-4a3277c1649b","task_key":"test--b6e3865b-127b-5f16-8b17-4a3277c1649b","task_revision_id":"1","upstream_id":"","short_description":"This question is a followup of part b. In this question, we no longer fix the…","config":"","split":"test","body":"{\"problem\":\"This question is a followup of part b. In this question, we no longer fix the route in part b but find one to maximize the carrier's profit. Suppose that the carrier receives a fixed reward of r for each delivery and spends \\\\ell, which equals the total lengths of the edges that s/he travels from pickup to delivery. In total, s/he makes a profit of r - \\\\ell on this delivery. (We have set the cost factor of travel distance to 1, for simplicity.) Suppose that the carrier just picked up the original order and has this order only. What is his/her optimal route assuming the scooter's trunk has a capacity of 2 orders? You shall consider both the travel distance as a cost and the possible additional profit of r for picking up a new order. Because any new order has the same destination, its travel cost is ignored. Also, suppose that 0 \\\\leq P_{e} \\\\leq \\\\min \\\\{\\\\ell_{e} / r, 1\\\\}, where \\\\ell_{e} is the length of edge e and P_{e} is defined in part b.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}