"Matlab解决夫妻过河问题的数学模型及应用研究"

The problem of couples crossing the river has been a logical challenge since the 8th century, and it remains a topic of interest in mathematics modeling textbooks. This problem involves different objects or organisms that cannot coexist with certain others, and the goal is to safely transport a small group from one side of the river to the other with no losses. The state transition problem in the couple crossing the river scenario does not always have a solution, and when it does, the solution may not follow a predictable pattern. In this study, the author, Guo Caihong, from the Mathematics and Information Science College at Qujing Normal University, explores the couple crossing the river problem using graphical methods and Matlab programming to determine if 5 pairs or 6 pairs of couples can safely cross the river. The study also extends to n pairs of couples and m boats to investigate the relationship between the number of couples and the boats' carrying capacity to ensure a safe crossing. The key words for this study include multi-step decision-making, Matlab, mathematical modeling, and the crossing river problem. This research sheds light on the complex nature of the problem and provides a systematic approach to finding solutions using computational tools.