The nutrients needed for crop growth in a certain area are mainly nitrogen (N), potassium (K) and phosphorus (P). A crop research institute has done a certain number of experiments on potatoes and lettuce in this area. The experimental data are shown in the table below, where ha stands for hectares and T stands for tons and kilograms. When the fertilization amount of one nutrient changes, the fertilization amount of another nutrient is always taken as the test morning, and the fertilization amounts of P and K are 196kg/ha and 372kg/ha respectively.
Potatoes: nitrogen, phosphorus and potassium
fertilizing amount
Output (kg/ha)
(ton/hectare)
fertilizing amount
Output (kg/ha)
Fertilization amount (ton/hectare)
Output (kg/ha)
(ton/hectare)
34
67
10 1
135
202
259
336
404
47 1
15. 18
2 1.36
25.72
32.29
34.03
39.45
43. 15
43.46
40.84
30.75
24
Forty nine
73
98
147
196
245
294
342
33.46
32.47
36.06
37.96
4 1.04
40.09
4 1.26
42. 17
40.36
42.73
47
93
140
186
279
372
465
258
25 1
18.98
27.35
34.86
38.52
38.44
39.73
38.43
43.87
42.77
65.22
Lettuce: nitrogen, phosphorus and potassium
fertilizing amount
Output (kg/ha)
(ton/hectare)
fertilizing amount
Output (kg/ha)
Fertilization amount (ton/hectare)
Output (kg/ha)
(ton/hectare)
28
Fifty-six
84
1 12
168
224
280
336
392
1 1.02
12.70
14.56
16.27
17.75
22.59
2 1.63
19.34
16. 12
14. 1 1
Forty nine
98
147
196
294
39 1
489
587
685
6.39
9.48
12.46
14.33
17. 10
2 1.94
22.64
2 1.34
22.07
24.53 0
47
93
140
186
279
372
465
558
65 1
15.75
16.76
16.89
16.24
17.56
19.20
17.97
15.84
20. 1 1
19.40
This paper attempts to analyze the relationship between fertilization amount and yield, and evaluate the results from the aspects of application value and how to improve it.
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Decomposition of experimental data in problem b
Several amino acids that make up the protein of life can form different combinations. When analyzing the composition of protein molecule by mass spectrometry, the first problem is how to decompose its molecular weight X into the sum of several amino acid known molecular weights A [I] (I = 1.2, ..., n). Among the problems studied in the laboratory:
n= 18，
a[ 1: 18]=57，7 1，87，97，99， 10 103， 1 13， 1 14， 1 1 15， 128，628
X is a positive integer ≤ 1000,
In view of whether there is a microcomputer in the laboratory, put forward your answers to the above questions, and discuss the mathematical models and methods generally discussed.
Topic of 2005 Higher Education Club Cup National Mathematical Modeling Competition for College Students
(Please read "Uniform Requirements for Paper Format" first)
Question A: Assessment and prediction of water quality in the Yangtze River.
Water is a resource for human survival. Protecting water resources means protecting ourselves, and the protection and management of water resources of major rivers in China should be the top priority. Experts called for: "People-oriented, building a civilized and harmonious society, improving the environment between man and nature and reducing pollution."
The Yangtze River is the largest river in China and the third largest river in the world. The water pollution in the Yangtze River is getting more and more serious, which has attracted the attention of relevant government departments and experts. From June 5438 to 10, 2004, the "Protecting the Yangtze River" investigation group, which was jointly composed of China People's Political Consultative Conference and China Development Research Institute, made a field trip to 2/kloc-0 key cities along the Yangtze River from Yibin in the upstream to Shanghai in the downstream, revealing the real picture of the pollution of the Yangtze River, and its pollution degree was shocking. To this end, experts put forward that "if it is not saved in time, the Yangtze River ecology will be on the verge of collapse within 10 years" (annex 1), and issued a call for "what to save the cancerous Yangtze River" (annex 2).
Annex 3 gives the detection data of main water quality indicators of 7 observation stations (regions) along the Yangtze River/Kloc-0 in recent two years, and the basic data (station distance, water flow and velocity) of 7 observation stations on the main stream in recent one year. It is generally believed that the water pollution of an observation station (region) mainly comes from local sewage discharge and upstream sewage. Generally speaking, the river itself has a certain natural purification ability for pollutants, that is, pollutants in the water environment can reduce the concentration of pollutants in water through physical degradation, chemical degradation and biological degradation. The index reflecting the natural purification ability of rivers is called degradation coefficient. In fact, the natural purification capacity of the main stream of the Yangtze River can be considered to be approximately uniform. According to the detection, the permanganate index and the degradation coefficient of ammonia nitrogen are usually between 0. 1~0.5, for example, 0.2 (unit: 1/ day) can be considered. Annex 4 is the main statistical data given in "1995-2004 Yangtze River Basin Water Quality Report". The following table shows the standard limits of four main items in the National Standard (GB3838-2002) Environmental Quality Standard for Surface Water, among which the first, second and third categories are drinking water.
Please study the following questions:
(1) The water quality of the Yangtze River in recent two years was evaluated quantitatively and comprehensively, and the water pollution situation in various regions was analyzed.
(2) Study and analyze the permanganate index and ammonia nitrogen pollution sources of the main pollutants in the Yangtze River in recent years.
(3) If more effective control measures are not taken, according to the main statistical data of the past 10, predict and analyze the future development trend of water pollution in the Yangtze River, such as studying the situation in the future 10.
(4) According to your prediction and analysis, if the proportion of Class IV and Class V water in the main stream of the Yangtze River is required to be controlled within 20% every year in the next 10 year, and there is no water worse than Class V, how much sewage will be treated each year?
(5) Do you have any practical suggestions and opinions on solving the water pollution problem in the Yangtze River?
Attached Table: Standard limit unit of four main items in Environmental Quality Standard for Surface Water (GB3838—2002): mg/L.
Serial number classification standard value items I, II, III, IV, V and worse than V.
1 dissolved oxygen (DO) ≥ 7.5 (or saturation rate 90%) 6 5 3 2 0
2 permanganate index (CODMn) ≤ 2 4 6 10 15.
3 ammonia nitrogen (NH3-N) ≤ 0.1.51.01.52.0
4 PH value (dimensionless) 6-9