陇东学院学报
隴東學院學報
롱동학원학보
JOURNAI OF LONGDONG UNIVERSITY
2011年
4期
7-10
,共4页
榆油管线%建设费用%数学模型%Newton迭代法%数学期望
榆油管線%建設費用%數學模型%Newton迭代法%數學期望
유유관선%건설비용%수학모형%Newton질대법%수학기망
oil pipeline%construction cost%mathematical model%Newton＇s Iteration method%Mathematical expectation
运用平面镜成像原理找到了修建车站的最佳位置，列出了输油管线长度的函数解析式．应用凸函数的一个性质和Newton迭代法找到了此函数的最小值点，从而求出了输油管线长度的最小值，建立了输油管线建设费用最省的一般数学模型．在此数学模型的基础上根据问题2的条件，给出了两套管线布置方案，求出了三家工程咨询公司估算的附加费用的数学期望，进而算出了管线布置方案的相应费用．根据问题3的条件从两套管线布置方案及相应的费用中筛选出了管线最佳布置方案及相应的费用．
運用平麵鏡成像原理找到瞭脩建車站的最佳位置，列齣瞭輸油管線長度的函數解析式．應用凸函數的一箇性質和Newton迭代法找到瞭此函數的最小值點，從而求齣瞭輸油管線長度的最小值，建立瞭輸油管線建設費用最省的一般數學模型．在此數學模型的基礎上根據問題2的條件，給齣瞭兩套管線佈置方案，求齣瞭三傢工程咨詢公司估算的附加費用的數學期望，進而算齣瞭管線佈置方案的相應費用．根據問題3的條件從兩套管線佈置方案及相應的費用中篩選齣瞭管線最佳佈置方案及相應的費用．
운용평면경성상원리조도료수건차참적최가위치，렬출료수유관선장도적함수해석식．응용철함수적일개성질화Newton질대법조도료차함수적최소치점，종이구출료수유관선장도적최소치，건립료수유관선건설비용최성적일반수학모형．재차수학모형적기출상근거문제2적조건，급출료량투관선포치방안，구출료삼가공정자순공사고산적부가비용적수학기망，진이산출료관선포치방안적상응비용．근거문제3적조건종량투관선포치방안급상응적비용중사선출료관선최가포치방안급상응적비용．
Directed at the problem put forward in this paper, locating the best position ot the station by plane mirror imaging principle, an analytic function for the length of oil pipeline has been drawn up. Finding the minimum point of the function by a property of convex function and Newton iteration method, accordingly, evaluating the minimum of the length of oil pipeline, a common mathematical model has been formed for the minimum cost of oil pipeline construction. Based on the mathematical model and the conditions given in question 2, providing two sets of plumbing plans, solving for the mathematical expectation of additional expense estimated by three engineering consulting companies, the corresponding cost of the plumbing plans has been worked out. Then, according to the conditions given in question 3, the best plumbing plan has been screened out of the two plumbing plans and their corresponding cost.
