Mathematical Modeling Questions! High score solicitation on the master!

Solution: Since the fuel cost per hour used by the ship is proportional to the cube of the ship's sailing speed, when the ship speed is 10 kilometers per hour, its fuel cost is 30 yuan per hour.

So the function of hourly cost and speed is f(v)=3 100*v 3+480 The total cost is f(v)=f(v)*1000 v, where v belongs to (0,25) Assuming that each steamer carries 400 passengers, the ticket ** is a function of speed.

It is obtained by 400*p-f(v)=400*10.

p(v)=[4000+f(v)]/400=[4000+(3/100*v^3+480)*1000/v]/400

10+30*v^2/400+1200/v

p'(v) = 60V 400-1200 V 2 When 0V > 20, p'>0

So the minimum ** is p(20)=100

So it is reasonable that ** is p>=100

Since it's mathematical modeling, it needs to be thoughtful:

The above results can be said to be applied locally.

I suggest that it would be reasonable to take the customer factor into account.

The number of customers directly affects revenue (and also affects**), and it is not necessarily feasible to control costs alone.

Therefore, I suggest that you use realistic data to simulate the functional relationship between customers and **. In addition, if you have time, you can also add more factors, such as increasing the speed change factor, etc.

If you are interested, you can discuss it together.

When adding, it is better to indicate it.

This result cites the results of some of the previous ones, thanks here).

Since the hourly fuel cost of the ship is proportional to the cube of the ship's sailing speed, when the ship's speed is 10 kilometers per hour, its fuel cost is 30 yuan per hour.

So the function of hourly cost and velocity is f(v)=3 100*v3+480

The total cost is: f(v)=f(v)*1000/v=3/10*v^2+480000/v

where v belongs to [0,25], and we can conclude by definition that f(v) is a monotonically decreasing function on [0,25].

Assuming that each ship carries 400 passengers, the ticket **p is a function of speed.

It is obtained by 400*p-f(v)=400*10.

p(v)=[4000+f(v)]/400=10+f(v)/400

On [0,25].

From the f(v) decrement knows the p(v) dwindling.

According to the general understanding, the so-called reasonable ** is to attract passengers with the most tempting ** (the lowest**), but without harming their own interests, as we know from the above analysis.

When v=25, the most reasonable ** can be obtained.

p(25)=15 32+48+10, so we can get a reasonable ** as the yuan.

Equation: Let the one-way fare x, then.

Income: 400x

Cost: Fuel rate per hour m=kv 3

k= is obtained from the known condition 30=k10 3

The total cost of one-way fuel c=m1000 v=30v 2. Other costs d=480*1000 V

Profit: y=400x-(c+d)=400x-(30v2+240000 v+240000 v).

30V 2 + 240000 V + 240000 V > = 3 cubic roots (30 * 240000 * 240000) = 36000

At this point v=20

Target y>=400*10

So x>=100 (yuan) is required

Equation: Can't figure it out.

The one-way fare is set at X yuan, and the speed is vkm h

Income: 400x

Fuel unit price: one-way fuel fee: 30*v 2

Other expenses: 480*1000 V

Profit: y=400x-30*v 2-480*1000 v30*v 2+480*1000 v=30*v 2+240000 v+240000 v>=3*(30*v 2*240000 v*240000 v) (1 3)=36000

v=20)y(max)=400x-36000 by the title: y>=4000

400x-3600>=4000

x>=100

Therefore, the speed is 20km h, and the ticket price is more than 100 yuan.

Set a one-way fare x, then.

Income: 400x

Cost: Fuel rate per hour m=kv 3

k= is obtained from the known condition 30=k10 3

The total cost of one-way fuel c=m1000 v=30v 2. Other costs d=480*1000 V

Profit: y=400x-(c+d)=400x-(30v2+240000 v+240000 v).

30V 2 + 240000 V + 240000 V > = 3 cubic roots (30 * 240000 * 240000) = 36000

At this point v=20

Target y>=400*10

So x>=100 (yuan) is required

Haha, such a simple question is also modeling, really good

Insulting to mathematical modeling, roar!

The math concludes that:

1 No matter what**, when the speed is 20 profit maximum.

2. When the price is 100 yuan and the speed is 20, the profit is exactly 10 yuan.

The reality is: it is difficult to maintain a constant speed when the ship is driven and stopped20

Still correct. The triangle BEP is similar to the triangle AFP is similar to the triangle ACB, so ab bc = bp pe = ap pf = ab pe + pf can be obtained pe + pf = bc

Therefore, the profit margin of the Spring Festival is high, 9% higher

10,000 yuan, the cost is 10,000 yuan profit.

40,000 yuan, the cost is 10,000 yuan, and the profit is high, high during the Spring Festival.

(1) Volume of water: cubic meters.

After lifting the iron rod 24 cm, immerse it in water The volume of the iron rod: cubic meters, the part of the iron rod immersed in water is: (cm.

2) The volume of gravel in the middle pool: cubic meters.

Volume of gravel in a small pool: cubic meters.

Total gravel: cubic meters.

Then the height of the large pool is raised: m = cm.

3) Volume of water: 72* cubic centimeters.

Assuming that the water depth height is a, according to the conditions: (6x6a+180)=72a, then: a=5 cm 6 cm, the water will not overflow, and the condition (4) the bottom area of the cuboid: square decimeters.

Then the bottom area of the cylinder is: square decimeters.

Assuming that the two containers are equal in height and a, there is.

Then a = 9 decimeters.

5) Let the rabbit be a and the chicken be b, then there is (a + b) (4a + 2b) = 2 5 then b a = 3 1 that is, the number ratio of chickens and rabbits is 3:1 ok After answering, I hope to give more points Hehe.

After checking, my answer was completely correct lol.

It's hard to write about ...... phoneHigh school students should be, so why don't you ask the people around you?

I'm scared to death, I haven't even heard of Poisson distribution and negative exponential distribution.

Suppose the investment in the project is billion, then the model.

Objective Function: max Constraint Function:

x1 <= 5

x2 <= 2

x3 <= 6

x4 <= 4

x5 <= 6

x6 <= 8

xi=22xi >= 0, i = 1,2,3,4,5,6