Questions and answers related to travel and mathematics

Best travel route design through mathematical modeling

Mr. Wang and his wife are young teachers at a university in East China and plan to travel to Xinjiang during the summer vacation. Influenced by literary works, Tianchi, Dabancheng, Turpan, Loulan Ancient City, and Yili are all places they yearn for. Other places in Xinjiang are also very attractive to them.

1. Please design a suitable travel itinerary for them so that they can visit as many places as possible with the least money during one month of this summer vacation, and estimate the expenses other than meals.

2． If they plan to complete their travel to Xinjiang during the summer vacation this year or next, please design a suitable travel route for them to save transportation costs within Xinjiang as much as possible.

3． If the National Minority Research Institute of a university in East China organizes a cultural inspection of Xinjiang, and the inspection is divided into three groups, the time spent on transportation is the same as in the first two cases, but the inspection time is four times the time for sightseeing, please design a suitable plan for them inspection route to complete the inspection mission as soon as possible.

4. In order to welcome the "May Day Tourism Golden Week" (taking into account long-distance travel, the travel within the autonomous region has been extended to 12 days), the tourism department of the Xinjiang Autonomous Region is preparing to organize multiple travel routes for tourists from outside the autonomous region to disperse tourists and improve the quality of reception. Under the assumption that the number of tourists participating in each route you designed is proportional to the reception capacity of the entire route, please design appropriate all tourist routes for the tourism department of the Xinjiang Autonomous Region and prepare to promote them to tourists.

The picture below shows the distribution map of Xinjiang’s main tourist attractions. Information such as the distance between tourist spots and the best stay time for each tourist attraction can be found on the Xinjiang Tourism Network. You can also further improve the questions.