Chapter 23: Classic modeling problems for businessmen and followers

Looking at the two people in the classroom, Professor Liu Xiangping gave a slight slump and asked with a smile: "Is there only two? I heard there is one more."
"... I'll call her and ask her." Wang Xiaodong looked awkward and went outside with the phone.
The teacher was not in a hurry. He unscrewed the thermos cup, took a sip of hot water, walked slowly to the side of Lu Zhou, and asked with a smile, "What is the configuration of your team?"
Lu Zhou put down his phone and replied with a smile: "I'm in charge of modeling, Wang Xiaodong is in charge of programming, Lin Yuxiang is in charge of writing thesis and defending."
"Modeling, programming, writing, standard configuration," Mr. Liu smiled, and continued, "Speaking of which, you are the Luzhou one or three times. I read your paper and it is indeed a good one. Article. "
Lu Zhou's eyes brightened: "Teacher, you also do math?"
"That's right, but my research direction is focused on physics, and mathematical papers are rarely published." Teacher Liu narrowed his eyes, glanced at the classroom door, and continued with a smile, "You lesbian, it seems not to be very reliable what."
Lu Lu smiled awkwardly and politely.
Teacher Liu also smiled, didn't say much on this issue, paused for a while, and then continued: "About the configuration of your team, I suggest that you can adjust it slightly. The modeling and thesis are the same person, and the rest Two people are responsible for programming. The advantage of this is that the person in charge of modeling has a strong grasp of the overall problem and the flow of ideas is smoother. However, of course, there are also disadvantages, that is, your burden will be heavy. The total time is only Three days, that means you have to start writing the dissertation right after you finish modeling. "
Lu Zhou thoughtfully: "... Are two people responsible for programming?"
抿 Teacher Liu took a sip of tea and said slowly: "Yes."
Lu Zhou smiled, but did not immediately respond: "I think about it again, after all, we have to discuss it with our teammates."
At this time, there were trotting footsteps outside the corridor, and the last teammate was finally overdue.
"I'm sorry, I got up a little late, I'm really sorry!" Entering the classroom with Wang Xiaodong, Lin Yuxiang bowed his head to the teacher with apologetic confession.
"It's okay, now that everyone is here, let's start quickly." Teacher Liu Xiangping smiled at ease and did not blame her for being late. She turned and walked to the podium, inserted the U disk into the computer, and opened it. The projector, released his PPT.
"Before starting the lecture, I hope you will look at an example problem. This problem is not difficult in itself, but it can be used as a case of mathematical modeling. I hope that through this set of cases, you can first understand what mathematical modeling is. what?"
He said, he pressed the mouse to turn the ppt to the next page.
"Three businessmen each took an entourage to cross the river by boat, and a boat could only accommodate two people. The entourages secretly said that on any bank of the river, once the number of entourages exceeds the number of merchants, they would kill people and buy more goods, but how to cross the river by boat. The power of businessmen is in the hands of businessmen, asking: How can businessmen cross the river safely? "
Indeed, there is no difficulty in this question.
Even without relying on the power of the system, Lu Zhou quickly came up with the answer and replied.
"In the first round, two followers passed by and one came back."
"In the second round, two followers passed by and one came back."
"In the third round, two businessmen passed by, one entourage and one merchant returned."
"In the fourth round, two businessmen passed by, and one of them followed."
"Fifth round, two followers pass by, and one follower returns."
"Sixth round, the last two followers passed and successfully crossed the river!"
"Papapa!" Lin Yuxiang clapped his hands and raised his hands in a low voice, his face full of worship.
The expression on Wang Xiaodong's face was unmoved, and he looked like a stranger.
In his opinion, this question is really not difficult. Although he didn't use his brain to figure it out, he believes his IQ and can at least take a little time to solve it.
"Exactly correct." Teacher Liu smiled and continued, "Even without any mathematical knowledge, this problem can be solved by logical analysis alone. But what if the problem is generalized to N businessmen?"
问题 This problem is indeed difficult, but it is not difficult to solve it in mathematics, but in how to abstract this problem into a mathematical problem.
Lu Zhou pondered for a while, and had a rough idea in his head.
"Can I use the blackboard?"
当然 "Of course," Professor Liu Xiangping smiled and made a please gesture.
Lu Zhou stepped forward, picked up chalk and started writing on the blackboard.
【①Remember that the number of merchants on this bank before the kth crossing is Xk. The number of followers is Yk, k = 1, 2, ..., Xk, Yk = 0, 1, 2, 3. The two-dimensional vector Sk = (Xk, Yk) is defined as the state, and the set of states under the condition of safely crossing the river is the set of allowed states, denoted by S.
We get S = {(X, Y)
X = 0, Y = 0,1,2,3; X = 3, Y = 0,1,2,3; X = Y = 1,2}
② Record the number of merchants on the k-th ferry as Uk and the number of followers as Vk. The two-dimensional vector Dk = (Uk, Vk) is defined as a decision. Allow the decision set to be recorded as D, which can be known from the capacity of the boat: D = {(U, V)
1≤U + V≤V, U, V = 0, 1, 2}
③ Based on the above conclusions, the change law of state Sk with Dk is: S (k + 1) = Sk + (-1) ^ k Dk
]
"It's amazing ..." Looking blankly at the blackboard on the blackboard, Lin Yuxiang opened his mouth slightly, looked at Lu Zhou coming down from the podium, and whispered in surprise, "Don't you need to make a draft?"
"Have a good fight in my heart." Lu Zhou said with a smile.
晓 Wang Xiaodong is also very silent as always, without speaking.
However, judging by his expression, this proud Xueba is completely convinced of Lu Zhou's mathematical ability.
Looking at the process on the blackboard, Professor Liu Xiangping nodded with a smile: "Exactly! But from the perspective of mathematical modeling, this work can only be half done. After completing the modeling, we still A program is needed to implement this model. Of course, this model is very simple. I believe that with the ability of our classmate Wang, this level of program must be hand-held, so we will not waste precious time here. "
晓 Wang Xiaodong pushed his glasses, the expression on his face was still indifferent, as it was of course.
Although he didn't have the opportunity to show his programming skills on the spot, it made him a little regrettable.
After a pause, Teacher Liu continued, "Data modeling is actually the process of simplifying an actual problem into a problem that can be expressed in data and very short language, and then solving this problem through mathematical tools ~ www. EbookFREE.me ~ So the key is what are the actual issues your team will face? "
"Modeling is not an investigation of the team's programming ability or mathematical ability, but an ability to translate actual problems into data languages ​​and solutions. You must remember this."
"I don't have much suggestions about modeling itself. There are no more shortcuts besides practicing and broadening the knowledge. As far as programming is concerned, I can say a few words."
"There are four main types of software, Mathematica, Lingo, and SAS. You don't need to master all of them. You can master at least one of them. The key is to use software that is suitable for you to solve practical problems." When saying this, Professor Liu Xiangping is looking at Wang Xiaodong.
Because this sentence is mainly for him.
晓 Wang Xiaodong pushed his glasses and nodded, "I have used it with SAS, and the problem is not big."
Professor Liu nodded his head: "It will be enough for these two softwares. These things need to be taught by you. What I can do is provide guidance when you don't understand."
最后 "Finally, it is about reference books. I recommend that you read some mathematical modeling cases, such as" Mathematical Model "," Mathematical Modeling Algorithms and Applications ", and" Basic Tutorial of Mathematical Modeling. "
"I also have some lectures and materials inside the school here, you can copy it back to see it, but remember not to circulate it, let alone upload it online. Understand?"
"I understand!" The three of them said in unison.
Professor Liu smiled and said, "Okay, that's all for today, I have nothing else to say, mainly on your own. If you need the information, please download it for me, and then go back to review English after finishing it. . "