{"task": {"agent_timeout": 600, "task": "omnimath_1630", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nThis 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.\n\n## Instructions\n\nSolve the mathematical problem above and write your final answer to `/workspace/answer.txt`.\n\n**Important**: Write only your final answer to the file, not the full solution process.\n\n### Guidelines\n\n- Provide your final numerical answer or mathematical expression\n- Write the answer as plain text (no special formatting needed)\n- Be precise and clear in your answer\n- The answer should directly respond to what the problem asks for\n\n### Example\n\nIf the problem asks \"What is 2 + 2?\", your answer file should contain:\n\n```\n4\n```\n\nYour answer will be evaluated against the correct solution using an automated grading system.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "math", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "omnimath", "tags": ["omni-math"]}, "runs": []}