Help me talk about this mathematical modeling problem with an answer .

Borrow a book on operations research in the library, Problems with Linear Programming.

Suppose the total distance traveled is x and the total cost is y, and you change to n taxis along the way, and the distance of the kth car is xk and the cost is yk

then x=x1+x2+.xn，y=y1+y2+..yn due to x1, x2 ,..xn has the same status, you might as well make 010, yk=9+7*, yk xk=, monotonically increasing.

Therefore, when xk = 10, the minimum value of the freight yk xk per hail kilometer = so the strategy of taking a taxi is to take a taxi to 10km, transfer to the next taxi, and so on.

Track racing, such as Formula 1, requires athletes to drive a car around the track for several laps. The track has a variety of curves of different shapes, and cornering technology is a key technology that reflects the level of driving of athletes. Based on the data given below, you can build a mathematical model and make your specific recommendations for athletes with different skill levels and driving styles.

Track width 18 m car width.

The weight of the car is 1500kg, and the maximum speed of the car is 280km h

The maximum output of the racing car is 1500 hp and the maximum braking force of the racing car is 40000N

The maximum lateral friction between the racing tyres and the track is 60,000N

The parameter reflecting the level of driving of an athlete is represented by the function = f ( s ), where s represents the braking distance of the car at its maximum speed before entering the corner on the straight, so that the car reaches the appropriate target speed when entering the corner. Since safety must be ensured, the difficulty of controlling the car is inversely proportional to the braking distances. Assuming that the speed v ( s ) of the car at the time of entering the corner is a random variable that obeys a normal distribution, representing the variance of the speed v (s ) of the car at the corner corresponding to the braking distance s, i.e. ( s ) = e(v ( s )-e ( v ( s ))2 , we take the following empirical formula:

s ) = + 500a s where s is in m and v (s ) is in km h and a reflects the athlete's level, assuming 1 a 2.

1.According to the limit of the maximum lateral friction, the maximum speed limit of the car on arc-shaped corners of different radii is given;

2.Establish a model to describe the speed of the car entering and exiting the corner, and give the calculation method of the time taken by the car to pass the corner.

3.Discuss the criteria for determining the optimal braking distance within the limits of absolute safety and in the probabilistic sense;

4.discuss the techniques available to overtake the riders in front of you in the corners;

5.Analyze the possible differences between the model and the actual situation, and make suggestions for improving the model.

Question B: Camping along the Yangtze River Visitors to the Big Long River (225 miles) can enjoy the scenery and invigorating rapids. Hikers can't reach the river, and the only way to get there is by rafting.

It takes a few days of camping. The river tour begins at First Launch and ends at Final Exit, with a total of 225 miles downstream. Travelers can choose between a rubber raft that relies on oars and a speed of 4 mph, or a motorboat that travels at 8 mph.

The tour starts to finishes and includes approximately 6 to 18 nights of camping in the river. The ** department in charge of managing the river wants to make every trip a great way to enjoy the wilderness experience while keeping as few encounters as possible with other boats in the river. Currently, there are X groups of tourists who pass through the Big Long River each year, and these rafting takes place in a period of 6 months, and the rest of the year is very cold and there will be no rafting.

There are Y camping sites on Big Long, evenly distributed across the river corridor. As the number of rafters increases, the regulator is asked that more boats should be allowed to drift. They decide how to arrange the best solution

This includes travel time (based on the number of nights spent on the river) and the choice of boat (motorbike or paddle boat) to make the best use of the campsite in the river. In other words, how many more rafting trips can Big Long River add during rafting season? The administrator expects you to give them the best advice on how to decide how much the river can accommodate, keeping in mind that no two groups of groups can occupy a campsite in the river at the same time.

Also, on one page of your summary sheet, prepare a one-page memo for managers describing your key findings.