National Mathematical Contest in Modeling A Problem Solution

Answer: 3,000 yuan a piece, do you want ?

You can refer to the Mathematical Modelling Network.

Now that you have the idea data and the model, start writing! Pressed for time.

(This answer may violate the Know the norm, check it later).

It's going to be handed over on Monday, bless you.

2013 Higher Education Society Cup National College Students Mathematical Contest in Modeling A Question Evaluation Points [Description] This point is for reference only, and the evaluation team of each competition area should independently review it according to the understanding of the topic and the students' answers.

The difficulty of this problem is to obtain the traffic flow data through the ** data, and establish a mathematical model based on this to analyze the relationship between the degree of road congestion and the upstream traffic volume after part of the lane is occupied. Please pay attention to the following aspects during the review: the preparation of modeling (the extraction of traffic flow data, including the processing of missing and errors), the establishment, solution and analysis methods of the model, the presentation of the results, the rationality analysis of the model and the expansion of the model.

When there is no queue of vehicles on the occupied road, the traffic capacity is equivalent to the situation of a single lane, but when there is a queue of vehicles on the occupied road, the traffic capacity of the road will be reduced due to the lane change of vehicles on the occupied road, and a good result should be clearly pointed out.

Due to the different demand of the downstream traffic flow direction of the accident cross section, the number of vehicles assigned to each lane upstream will be different, so that the probability of forming a multi-lane queue in the road cross section where the accident is located in the two situations is different, thereby affecting the actual traffic capacity. It would be better if this was noticed in the model.

A mathematical model is established to give the relationship between the queue length of the road section caused by the traffic accident and the actual traffic capacity of the accident cross section, the duration of the accident, and the upstream traffic flow of the road section.

3. 2.Models can come in a variety of forms, but they need to include all of the factors mentioned above. The key is to examine the rationality of the model's assumptions, the principles of parameter determination, and the computability of the model.

Problem: This problem is an extension of problem 1 and problem 3, and the traffic capacity obtained by problem 1 and the model calculation result of problem 3 can be used;

4.2 Different from the problem, when the accident cross section is close to the traffic light intersection, the driver does not have enough time to adjust the lane, which will increase the multi-lane occupation situation and affect the traffic capacity, which should be considered in the model calculation;

The attachment gives the controller of the upstream intersection signal light and the cluster case, which will affect the flow distribution of upstream vehicles, and it would be better if the students could use the attachment to give the upstream intersection signal timing scheme and traffic organization scheme.

Let y be the profit and x be the number of days when **, then the following equation can be listed:

y = （80 + 2x）* 8 - 5x = + 3x + 640

To find the maximum value of y, you can use the following two methods:

1.Derivation.

When the derivative is 0, y has a maximum value.

Order y'= x +3 = 0 then we find x = where x = 7 and y =

where x = 8 and y =

Therefore, selling on the 7th or 8th day can get the maximum profit.

2.Formulation.

y = -

Depending on the nature of the parabola, there are the highest points.

It can also be seen later that there is a maximum value at x = 7 or 8.

Question C Personal Analysis:

1. The first question is relatively simple, let you do **, choose the appropriate ** method (at the same time, pay attention to make appropriate assumptions, don't make some assumptions that you feel are inappropriate;But don't make assumptions about too much detail);For the search for ** methods, you can refer to the introduction in the "Encyclopedia of Modeling Ideas and Methods and Scope of Application".

When reviewing this question, it is necessary to stipulate that there must be some assumptions, and as for which assumptions, you should ponder for yourself

2. How to say this question, it is a calculation and processing of data, focusing on understanding some concepts, and choosing appropriate algorithms and software to solve, which will allow you to get twice the result with half the effort.

Note: There is a good chance that there is a range of answers to this question!

3. This problem is also a calculation problem, it is relatively simple, think about it yourself, focus on understanding some concepts, and match the data indicators with the concepts, which is the key;As long as it corresponds, it will be clearer to deal with;After all, there is a relevant calculation formula in the annex;

4. The fourth question is a semi-open question, and everyone considers different angles, so the measures taken by Cairuqiao Town are different;Don't do whatever it takes to achieve two goals: (1) to achieve the target replacement rate, and (2) to maintain the balance of pension insurance.