I have written a similar diary myself before. You can change it and take it away.

I. Introduction

I bought a crutch yesterday and found that a whole crutch costs four yuan. If I sell it in sections, it's one yuan each. The method of section is to divide a sugarcane into four sections according to the length and equal distance. However, due to the different thickness and sweetness of different parts of sugarcane, the purchaser is unfair, which is in great contradiction with our socialist distribution to pay attention to fairness and efficiency. Moreover, the edible value of sugarcane heads is small, which often leads to the inability to sell sugarcane heads and reduces the income of sugarcane farmers. As an important product in southern China, sugarcane is not only the only reliable source of income for sugarcane farmers, but also an important raw material for food industry, which plays an important role in agricultural production. President Hu once said that the problems of agriculture, rural areas and farmers are the fundamental problems in China, and increasing farmers' income is the foundation. In order to implement the spirit of the 17th National Congress of the Communist Party of China and President Hu's speech, and ensure the interests of the majority of sugarcane farmers and the fair distribution of socialism, this paper makes a preliminary calculation on the rationalization of sugarcane segmentation, and the calculation ideas are as follows:

1. Calculate the total sugar content of sugarcane.

2. Divide sugarcane into equal parts according to the total sugar content, which is the preliminary basis for sugarcane segmentation.

3. On the basis of 2, consider the cost of eating sugar cane (for example, the thicker the sugar cane, the more tired it is. ) and further rationalize the segmentation of sugarcane.

Two. theoretical model

(A) the total sugar content of sugarcane

1. Cross-sectional area formula

Let the functional relationship between sugarcane cross-sectional area and height be f(x), where x is height. It can be inferred from common sense that f(x) is the subtraction function of x, that is, f' (x).

f(x)=πr(x)？ =π(b-ax)？ ( 1)

2. Sweetness formula

Located at the height x, the sugar content per unit volume of sugarcane is g(x), and the total sugar content of sugarcane is u, so the total sugar content du at the height x is:

du=g(x)dv (2)

And dv=f(x)*dx (3)

According to formulas (2) and (3):

du=f(x)g(x)dx (4)

According to biological knowledge:

G(x) generally decays exponentially. When the height reaches a certain level h, the sugar content can be approximately considered as 0, so it can be set as follows:

Get:

From this, we get the sweetness formula of sugarcane:

This sweetness formula reflects the functional relationship between sweetness and height, and it can be seen from the formula that sweetness and height are obviously decreasing.

3. Total sugar content

Let's start to calculate the total sugar content u of sugarcane.

Calculation:

This is the total sugar content of sugarcane with length h.

(2) Segmenting the sugarcane.

Suppose that sugarcane is divided into n segments, and the sugar content of each segment is u/n.

There are:

Then each one can be deduced from the above formula.

Because I want to have lunch, this article will not be deduced for the time being. Interested students can do the math themselves.

Consider the cost of eating sugar cane

Suppose that the relationship between the pain degree of eating sugarcane and the cross-sectional area is linear, that is,

p(x)=m*g(x)

Then the enjoyment of eating sugarcane q(x)=u(x)-p(x)

That is, the degree of enjoyment is directly proportional to sweetness and inversely proportional to the degree of pain.

So obtained

Then use q(x) instead of u(x) in (2) to find out each hi, and then hi-h(i- 1) is the length of each paragraph.

Three. Conclusion and prospect

It can be seen from the above conclusions that in order to ensure the interests of the majority of sugarcane farmers and the fairness of consumers, the division of sugarcane should follow scientific principles and be reasonable.

Future work: As can be seen from the formula, the calculation in this paper is still rough, and the next step is to accurately measure the simulation function of sugar cane sweetness and pain by using statistical principles.