宁波大学2017年博士研究生招生考试初试试题(B卷)
(答案必须写在考点提供的答题纸上)
科目代码: 3825 科目名称：运筹学
第 1 页共2 页
运筹学试题研究生|运筹学研究生 中国矿业大学2010～2011学年第一学期研究生 《运筹学》试卷 一、（20分）某服装厂制造大、中、小三种尺寸的防寒服，所用资源有尼龙绸、尼龙棉、劳动力和缝纫设 备，不考虑固定费用，则每件防寒服售出一件所得利润分别为10、12、13元，可用资源分别为: 尼龙绸1500米、尼龙棉1000米、劳动力4000和缝纫设备3000小时。此外，每种防寒服不管缝制多少件，只要做都要支付一定的固定费用：大号200元、中号150元、小号100元。现欲制定一生产计划使获得的利润为最大，试写出其数学模型（不求解）。 二、(20分) 已知下述线性规划问题： max z =5x 1-x 2-x 3 ?-3x 1+x 2+x 3≤11 ? -x +x +x ≥3?123 ?x ≥0, i =1, 2, 3 i ? ①用大M 法求其最优解。②写出其对偶问题。 ③用三种方法求出其对偶问题的最优解。④求使最优解不变的c 2的取值范围。 三、（20分）某公司有资金10万元，若投资于项目i (i =1,2,3) 的投资额为x i 时，其收益函数分别为g 1(x 1)=4x 1， g 2(x 2)=9x 2，g 3(x 3)=x 32，又知其中项目1投资额不
能少于2万元，项目3投资额不能超过5万元，现需要分配投资额是总收益最大。为此① 试建立该问题的动态规划模型（指出阶段的划分、状态变量、决策变量、状态转移方程、指标函数、递推关系式）。七、（10分）某公司有资金10万元，若投资于项目i (i =1,2,3) 的投资额为x i 时，其收益函数分别为g 1(x 1)=4x 1，g 2(x 2)=9x 2，g 3(x 3)=x 32，又知其中项目1投资额不能少于2万元，项目3投资额不能超过5万元，现需要分配投资额是总收益最大。为此 ①试建立该问题的动态规划模型（指出阶段的划分、状态变量、决策变量、状态转移方程、指标函数、递推关系式）。② 用逆序法求出该问题的最优解。 四、（20分）对于如下生产计划问题： 某厂生产I ，II ，III 三种产品，都分别经A ，B 两道工序。设A 工序可分别在设备A 1和A 2上完成，有B 1，B 2，B 3三种设备可用于完成B 工序。已知产品I 可在A ，B 任何一种设备上加工，产品II 可在任何规格的A 设备上加工，但完成B 工序时，只能在B 设备上加工。加工单位产品所需工序时间及其它各项数据见下表： 1 该工厂计划期经营目标如下：①利润尽可能多； ②产品II 的产量要尽可能与产品I 的产量达到1:2的比例；③设备A 1和A 2的负荷（指加工产品时间）尽量保
考博英语历年真题 北大2013年考博士英语真题及答案 Part Two:Structure and Written Expression20 Directions:In each question decide which of four choices given will most suita bly complete the sentence if inserted at the place marked.Mark your choices on the ANSWERSHEET. 21.The nuclear family__________a self-contained,self-satisfying unit compose d of father,mother and children. A.refers to B.defines C.describes D.devotes to 22.Some polls show that roughly two-thirds of the general public believe that e lderly Americans are________by social isolation and loneliness. A.reproach ed B.favored C.plagued D.reprehended 23.In addition to bettering group and individual performance,cooperation_____ ___the quality of interpersonal relationship. A.ascends https://www.doczj.com/doc/9c947350.html,pels C.enhances D.prefers 24.In the past50years,there________a great increase in the amount of resea rch_____on the human brain. A.was…did B.has been…to be done C.was…doing D.has been…done 25. “I must have eaten something wrong.I feel like_____.”“We told you not t o eat at a restaurant.You’ d better_______at hom e when you are not in the shape.” A.to throw up… to eat B.throwing up…eating C.to throw up…eat D.throwing up…eat 26.Parent shave to show due concerns to their children’ s creativity and emotional output;otherwise what they think beneficial to t he kids might probably_______their enthusiasm and aspirations. A.hold back B.hold to C.hold down D.hold over 27.According to psychoanalysis,a person’ s attention is attracted________by the intensity of different signals____ ____by their context,significance,and information content. A.not less than…as B.as…just as C.so much…as D.not so much… as28.They moved to Portland in1998and lived in a big house,_______to the south. A.the windows of which opened B.the windows of it opened C. its windows opened D.the windows of which opening 29.The lady who has_______for a night in the dead of the winter later turned o ut to be a distant relation of his. A.put him up B.put him out C.put him on D.put him in30.By standers, _______,_________as they walked past lines of ambulances. A.bloody and cov ered with dust,looking dazed B.bloodied and covered with dust,looked daze
中国人民解放军后勤工程学院 2014年攻读博士学位研究生入学考试 试题 考试科目（代码）：运筹学（2004）共3页 答案必须写在考点发放的答题纸上，否则不记分 一、判断题（每小题2分，共20分） [1]对或的排队系统，服务完毕离开系统的顾客流也为泊松流。( ) [2]对偶问题的对偶问题一定是原问题。（） [3]当所有产地产量和销地的销量均为整数值时，运输问题的最优解也为整数值。( ) [4]在任一图G中，当点集V确定后，树图是G中边数最少的连通图。（） [5]线性规划模型中增加一个约束条件，可行域的范围一般将缩小；减少一个约束条件，可行域的范围一般将扩大。( ) [6]线性规划可行域的某一顶点若其目标函数值优于相邻的所有顶点的目标函数值，则该顶点处的目标函数值达到最优。( ) [7]单纯形法计算中，选取最大正检验数对应的变量作为换入变量，将使目标函数值得到最快的增长。( ) [8]线性规划的模型是目标规划模型的特殊形式。( ) [9]用单纯形法求解标准形式（求最小值）的线性规划问题时，与对应的变量都可以被选作换入变量。( ) [10]一个动态规划问题若能用网络表达时，节点代表各阶段的状态值，各条弧代表了可行的方案选择。( ) 二、问答题(每小题5分,共10分) [1]某医院订购体温计。订购价同一次订购数量Q有关，当Q<800时，每支12.0 0元，当Q>=800时，每支8.00元，年存贮费为订购价的25％。若分别用和 代表订购价为12.00元和8.00元时的最优订货批量，说明。 [2]某街道口有一电话亭，在步行距离为4 min的拐弯处有另一电话亭。已知每次电话的平均通话时间为3分钟，服从负指数分布，又已知到达这两个电话亭的顾客均为10个／小时的普阿松分布。假如有名 1
2014年上海海事大学攻读硕士学位研究生入学考试试题 （重要提示：答案必须做在答题纸上，做在试题上不给分） 考试科目代码 809 考试科目名称 运筹学 一、名词解释（每道题4分，共20分） 1.剩余变量 2.影子价格 3.对策论 4.运输规划 5.排队论 二．论述题（每道题10分，共40分）： 1.线性规划有何特点，线性规划求解的基本思想是什么？(10分) 2.港口近年来发展迅速，但也暴露出了许多港口建设无序、恶性竞争的现象。利用对策论分析港口合作竞争。(10分) 3. 用运筹学理论解释“谋事在人，成事在天”论断。（10分） 4. 列举决策树方法的优缺点。（10分） 三、计算题或证明题 1. (本题满分25分) 考虑某生产计划优化的线性规划问题（P ） ???≥≤=0 ..max X b AX t s CX Z （1）写出其互补松弛（松紧）性质；(10分) （2）由互补松弛性质说明：在最优计划下，如果（P ）中第j 种资源没有得到充分利用，则该资源的影子价格一定等于零；如果第i 种产品安排投产了，则该产品的机会成本（隐含成本，即少生产一件
该产品所节省的资源可以增加的价值）一定等于其产值（价格系数）。(15分) 2. (本题满分20分) 考虑矩阵对策{}A S S G ,,21=，其中 3 142322 31=A 求最优策略 3. （本题满分20分） 试分析以下参数线性规划问题。当参数0≥t 时的最优解变化。 ???????≥≤+≤≤-++=0 ,18 2364)210()46(max 2121212 1x x x x x x x t x t t z ）（ 4. （本题满分25分） 证明：一个[]3//M M :[]FCFS //∞∞的排队系统要比三个[]1//M M :[]FCFS //∞∞的排队系统优越。试从队长L 这个指标证明。
Reading Comprehension (35 minutes) Directions:There are 4 reading passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A), B), C) and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the center. Passage One Questions 21 to 25 are based on the following passage: When Kathie Gifford ’s face was splashed across the newspapers in 1996 after her lucrative line of Wal mart clothing was exposed as the work of underpaid laborers in New York City ’s Chinatown, the Department of Labor and the White House teamed up to condemn such practices. With much fanfare, President Clinton’s administration launched the “No Sweat” campaign, which pressured retailers and manufacturers to submit to periodic independent inspection of their workplace conditions.; This campaign urged manufacturers to sign the Workplace Code of Conduct, a promise to self regulate that has since been adopted by a handful of retailers and many of the nation ’s largest manufacturers, including Nike and L.L. Bean. However, the Department of Defense, which has a $ 1 billion garment business that would make it the country’s 14th largest retail apparel outlet, has not signed the Code of Conduct. In addition, it has not agreed to demand that its contractors submit to periodic inspections.; Because the Department of Defense has not agreed to adhere to the code, the job of stopping public sector sweatshops falls to the Department of Labor. Federal contractors that persist in violating wage laws or safety and health codes can lose their lucrative taxpayer financed contracts. But Suzanne Seiden, a deputy administrator at the Department of Labor, says that to her knowledge, the department has never applied that rule to government apparel manufacturers. “I just assume that they are adhering to safety and health requirements,” she says. According to records obtained by Mother Jones, through a Freedom of Information Act request, the Occupational Safety and Health Administration has cited Lion 32 times for safety and health violations in the past 12 years. 21.What is this passgage mainly concerned with? A)The functions of the Department of Labor in America. B)A serious problem threatening American economy. C)The successful attempt of regulating sweatshops in America. D)The seriousness of the problem of sweatshops in America. 22.According to the passage, Kathie Gifford ____. A) was one of the underpaid laborers in New York City’s Chinatown B) was one of the well paid laborers in New York City ’s Chinatown C) made much money from cheap laborers in New York City’s Chinatown D) wrote a newspaper article exposing the practice of employing cheap laborers 23.The underlined p hrase “to submit to” is closest in meaning to ____. A) to accept unwillingly B) to refuse coldly C) to welcome warm heartedly D) to blame strongly 24.Which of the following statements about the Department of Defense is true? A) It will become the count ry’s 14th largest retail apparel manufacturer. B) It hasn’t acted according to the Workplace Code of Conduct. C) It has demanded its contractors to sign the Workplace Code of Conduct. D) It has teamed up with the Department of Labor to launch a campaign. 25.What was the purpose of President Clinton’s administration launching the “No Sweat” campaign? A) To urge manufacturers to obey the Workplace Code of Conduct. B) To remind the manufacturers of the Workplace Code of Conduct. C) To urge the Department of Labor to take its responsibility. D) To urge the Department of Defense to inspect manufacturers. Passage Two Questions 26 to 30 are based on the following passage: The term investment portfolio conjures up visions of the truly rich-the Rockefellers, the Wal Mart Waltons, Bill Gates. But today, everyone-from the Philadelphia firefighter, his part time receptionist wife and their three children, to the single Los Angeles lawyer starting out on his own-needs a portfolio.; A portfolio is simply a collection of financial assets. It may include real estate, rare stamps and coins, precious metals and even artworks. But those are for people with expertise. What most of us need to know about are stocks, bonds and cash (including such cash equivalents as money market funds).; How do you decide what part of your portfolio should go to each of the big three? Begin by understanding that stocks pay higher returns but are more risky; bonds and cash pay lower returns but are less risky.; Research by Ibbotson Associates, for example, shows that large company stocks, on average, have returned 11.2 percent annually since 1926. Over the same period, by comparison, bonds have returned an annual average of 5.3 percent and cash, 3.8 percent.; But short term risk is another matter. In 1974, a one year $1000 investment in the stock market would have declined to $735.; With bonds, there are two kinds of risk: that the borrower won’t pay you back and that the money you’ll get won’t be worth very much. The U.S. government stands behi nd treasury bonds, so the credit risk is almost nil. But the inflation risk remains. Say you buy a $1000 bond maturing in ten years. If inflation averages about seven percent over that time, then the $1000 you receive at maturity can only buy $500 worth of today’s goods.; With cash, the inflation risk is lower, since over a long period you can keep rolling over your CDs every year (or more often). If inflation rises, interest rates rise to compensate.; As a result, the single most imortant rule in building a portfolio is this: If you don’t need
1/4 【育明教育】中国考研考博专业课辅导第一品牌官方网站：https://www.doczj.com/doc/9c947350.html, 开设课程：【网络函授班】【精品小班】【高端一对一】【状元集训营】【定向保录】 【育明天津分校】相信未来，相信花开！ 12015年天津大学考研13年天津大学832运筹学基础考研试题运筹学基础考研试题专业课学术型考生做一至七题，全日制专业学位型考生做一至六和八题。 一、选择题18’ 1、运筹学是一门以____技术为主要工具，为管理决策提供科学依据的____ 科学，其核心思想是____。 A、定量，基础，整体优化 B、定量，技术，整体优化 C、定量，工程，系 统工程D、定性，哲学，系统观 2、下述这些图形阴影部分都是一些数学模型可行域，则____描述是正确的。 A、Ⅰ、Ⅱ是线性规划可行域，但Ⅲ、Ⅳ不是线性规划可行域 B、Ⅱ、Ⅲ是线性规划可行域，但Ⅰ、Ⅳ不是线性规划可行域 C、Ⅰ、Ⅱ、Ⅲ是线性规划可行域，但Ⅳ不是线性规划可行域 D、以上四个都不正确 3、下列____不是EOQ 库存模型的影响要素。A、需求率B、订货量C、存 储费D、缺货费 4、对于M/M/1/8/∞排队系统，若已知稳态时顾客平均到达率为λ，服务机 构的平均服务率为μ，系统状态概率为Pi（i=0,1,…,8），则稳态情况下，系统
2/4 【育明教育】中国考研考博专业课辅导第一品牌官方网站：https://www.doczj.com/doc/9c947350.html, 开设课程：【网络函授班】【精品小班】【高端一对一】【状元集训营】【定向保录】 【育明天津分校】相信未来，相信花开！ 2的有效到达率为____。A、λ(1-P8)B、λC、λ(1-P0)D、μ（1-P8） 5、某人收益为x 的效用为μ(x)，若μ(x)对x 边际递增，则他对风险的态 度____。A、风险中立B、厌恶风险C、追求风险D、无法确定 6、设R 是服从[0,1]区间上____分布的随机变量，X 的分布函数为Fx(x)， 则x=____。A、0-1， 二，建立线性规划模型，一个工件A，加工需要经过B1,B2,B3三个工序， 给出了B1和B2的约束时间，B3有两种方式B31和B32，只能选择一种，问怎样才能是利润最大。都为整数。 三，动态规划，有两问，只需回答一问就行，一共有a 吨的原材料，分配 Xj 吨给j 产品的收益是g(Xj)，j=1,2,3,……N,问怎样分配使收益最大，建立模型，写出状态变量，决策变量，状态转移方程，递归方程等等。。。 第二问是给出了a=3还是2来着，求解即可。 四，网络计划，这题好像32分，好贵，不过挺常规的，关键路线，预期工 期，还有调整啥的使费用最低。 五，存储论+随机模拟，不过给出了模拟数，以及模拟数对应的需求量和订 货周期，跟MRP 的题目差不多。求平均成本，填完表格。
育明考博 免费咨询报名电话：400-668-6978咨询QQ：493371626（李老师） 2015考博QQ交流群105619820 2015考博QQ英语群335488903 2015考博QQ专业课群157460416 2015长安大学考博英语分析 一、招考介绍 从整体上看，由于博士生招生形势的不断发展各院校博士生入学考试的难度越来越大，对考生的外语水平要求也越来越高，特别是听、说能力。攻读博士学位的学生，一方面应该具备坚实的专业理论基础和扎实的科研能力，另一方面还应该具备较高水平的外语能力。 二、联系导师 在初步定好考博学校之后，就要和所报考院校中意的老师取得联系，询问是否有招生名额，能否报考，这是我们考博成功的关键第一步。 大多数考生会在九月中下旬与导师取得联系。因为太早，学校里面直博名额什么的还没有确定，报考的导师也不清楚是否有名额；太晚的话，怕别的学生比你早联系就不好了。一般情况下，导师对一个学生很中意的话，后来联系的学生，导师一般也不会答应其报考了。在此说点题外话，联系导师的过程中，如果读研期间的导师有关系，可以尽量利用。如果没有，也没关系，凭着自己的本事也是可以和考博导师很好的沟通的，这就要看自己了。 通常跟导师初次联系，都是发邮件。导师回复邮件的情况一般有几种： （1）、欢迎报考。这种答复最笼统，说明不了问题。我们可以接着努力和老师多沟通，看看具体的进展，避免出现初试之后却没有名额的情况。 （2）、名额有限，可以报考，但有竞争。很多人说这样的回复不满意，认为希望很小一般会被刷。其实这样还是比较好的一种回答，最起码导师没有骗你而且给你机会去证明自己，考的好就可以上。 (3）、你的研究方向和我一样......各种一大堆他的研究方向和你相关，欢迎报考什么的话。不
（用于09级本科） 一、单项选择题（每题3分，共27分） 1. 使用人工变量法求解极大化的线性规划问题时，当所有的检验数0j δ≤,但在基变量中仍含有非零的人工变量，表明该线性规划问题( D ) A ．有唯一的最优解 B ．有无穷多最优解 C ．为无界解 D ．无可行解 2.对于线性规划 12 1231241234 max 24..3451,,,0z x x s t x x x x x x x x x x =-+-+=?? ++=??≥? 如果取基1110B ?? = ???，则对于基B 的基解为（ B ） A.(0,0,4,1)T X = B.(1,0,3,0)T X = C.(4,0,0,3)T X =- D.(23/8,3/8,0,0)T X =- 3.对偶单纯形法解最小化线性规划问题时，每次迭代要求单纯形表中（ C ） A ．b 列元素不小于零 B ．检验数都大于零 C ．检验数都不小于零 D ．检验数都不大于零 4. 在n 个产地、m 个销地的产销平衡运输问题中，( D )是错误的。 A ．运输问题是线性规划问题 B ．基变量的个数是数字格的个数 C ．非基变量的个数有1mn n m --+个 D ．每一格在运输图中均有一闭合回路 5. 关于线性规划的原问题和对偶问题，下列说法正确的是（ B ） A ．若原问题为无界解，则对偶问题也为无界解 B ．若原问题无可行解，其对偶问题具有无界解或无可行解
C ．若原问题存在可行解，其对偶问题必存在可行解 D ．若原问题存在可行解，其对偶问题无可行解 6．已知规范形式原问题（max 问题）的最优表中的检验数为12(,,...,)n λλλ，松 弛变量的检验数为12(,,...,)n n n m λλλ+++，则对偶问题的最优解为（ C ） A. 12(,,...,)n λλλ B. 12(,,...,)n λλλ--- C ．12(,,...,)n n n m λλλ+++--- D. 12(,,...,)n n n m λλλ+++ 7.当线性规划的可行解集合非空时一定（ D ） A.包含原点 B.有界 C ．无界 D.是凸集 8.线性规划具有多重最优解是指（ B ） A.目标函数系数与某约束系数对应成比例。 B ．最优表中存在非基变量的检验数为零。 C ．可行解集合无界。 D ．存在基变量等于零。 9．线性规划的约束条件为1231241234 2224,,,0x x x x x x x x x x ++=?? ++=??≥?，则基可行解是（ D ） A.(2,0,0,1) B.(-1,1,2,4) C.(2,2,-2,-4) D.(0,0,2,4) 二、填空题(每题3分，共15分) 1．线性规划问题中，如果在约束条件中没有单位矩阵作为初始可行基，我们通常用增加 人工变量 的方法来产生初始可行基。 2.当原问题可行，对偶问题不可行时，常用的求解线性规划问题的方法是 单纯形 法。 3.原问题的第1个约束方程是“=”型，则对偶问题相应的变量是 无约束 变量。 4.运输问题中，当总供应量大于总需求量时，求解时需虚设一个_销__地，此地的需求量为总供应量减去总需求量。 5. 约束121212264612420x x x x x x +≤+≥+≤,及中至少有一个起作用，引入0-1
考博英语（阅读理解）历年真题试卷汇编3 (总分：40.00，做题时间：90分钟) 一、Reading Comprehensio(总题数：4，分数：40.00) The United Nations Population Fund has picked October 31 as the day the world will be home to 7 billion people. For better and worse, it's a milestone. And there will be more milestones ahead. Fourteen years from now, there are expected to be 8 billion people on the planet. Most of the growth will occur in the world's poorer countries. Proportionally, Europe's population will decline, while Africa's will increase. At around the same time, India will overtake China as the most populous nation on Earth. The growing global population is just one side of the coin. A recent report from the World Health Organization signaled the seriousness of the human population explosion: more than 3 billion people — about half the world's population — are malnourished. Never before have so many, or such a large proportion, of the world's people been malnourished. And in a growing number of countries there is a seemingly unstoppable march toward sub-replacement fertility, whereby each new generation is less populous than the previous one, and population aging. As a result of declining fertility and increasing longevity, the populations of more and more countries are aging raging rapidly. Between 2005 and 2050, a rise in the population aged 60 years or over will be visible, whereas the number of children(persons under age 15)will decline slightly. Population aging represents, in one sense, a success story for mankind, but it also poses profound challenges to public institutions that must adapt to a changing age structure. The latest national census in China shows the number of elderly people in the country has jumped to more than 13. 3 percent of the population, an increase of nearly 3 percentage points on the percentage from the previous census in 2000. A quarter of the country's population will be over 65 by 2050, according to the National Population and Family Planning Commission. The growing number of elderly is a challenge that the government needs to tackle, we can't rely on the ever-increasing population to support them or maintain the nation's economic growth. Better solutions are needed, such as raising retirement ages to reflect the greater longevity and working capability of today's older adults and making adjustments so pension programs are more accessible. It was heartening to hear the Ministry of Human Resources and Social Security spokesperson announced in Beijing on Tuesday that the government will take retirement policy seriously and proactively. Shanghai began testing a flexible retirement system last October. Eligible employees in the private sector are allowed to postpone retirement until the age of 65 for men and 60 for women. Public servants, however, will continue to retire under the present system age 60 for men and 55 for women.（分数：10.00） (1).According to the passage, India will______in 14 years.（分数：2.00） A.be a poorer country B.be the most populous country C.decline in population D.increase investment in Africa (2).What problem will result from the global population explosion?（分数：2.00） A.Population aging. B.Increasing longevity. C.Declining fertility. D.Expanding malnourishment. (3).Population on aging represents the following EXCEPT______.（分数：2.00） A.rapid economic development B.challenge to public in institutions C.success story of mankind
考生注意考生注意：：本试卷共九大题本试卷共九大题，，满分150分。考试时间为3小时小时；； 所有答案均写在答题纸上所有答案均写在答题纸上，，在此答题无效在此答题无效。。 一．填空题填空题（（本题共10小题小题，，每小题3分，满分30分） （1）已知线性规划问题：min z =4x 1+5x 2+9x 3 x 1+ x 2 +2x 3 ≤16 st. 7x 1+5x 2+3x 3 ≥25 x 2 -6x 3 =10 x 1≥0,x 2 ≤0,x 3 为自由变量 其对偶问题为 。 （2）完全不确定情况下的决策方法有 ， ， 。 （3）运输问题表上作业法中空格检验数的经济意义是 。 （4）线性规划模型中，松弛变量的经济意义是 ，它在目标函数中的系数是 。 （5）设有线性规划问题：max z=CX AX ≤b X ≥0 有一可行基B ，记相应基变量为X B ,非基变量为X N ，则可行解的定义为 ，基本可行解的定义为 ，B 为最优基的条件是 。 （6）在产销平衡的运输问题中，基变量的个数为 ，用表上作业法求解时，表中空格数是 （设有m 个产地，n 个销地）。 （7）判别网络最大流的条件是 。 （8）已知赋权网络图为： 6 8 10 1 4 5 则其最小支撑树的权和为 。 （9）在绘制网络计划图时，不允许出现的图形有 ， ， 。 （10）线性规划模型的可行域的顶点与基本可行解的个数 ，若其有最优解，必能在 上获得。因此，
单纯型法是在 解中寻优。 二．选择题选择题（（本题共5小题小题，，每小题3分，满分15分） 说明说明：：在每题的备选答案中在每题的备选答案中，，选择一个正确答案选择一个正确答案。。 （1）记线性规划 原问题（p ）max z=CX ， 对偶问题（D ） min w=Yb AX ≤b YA ≥C X ≥0 Y ≥0 现用单纯形表解（P ）求得最优解，则在最优单纯形表中，同时也可得到（D ）的最优解，它应等于： （a ）表中松弛变量的检验数 （b ）表中松弛变量的检验数的负值 （c ）表中非基变量的检验数 （d ）表中非基变量的检验数的负值 （2）若运输问题已求得最优解，此时所求出的检验数一定是全部： (a)大于或等于零 (b)大于零 (c)小于零 (d)小于或等于零 （3）目标函数取极大（max z ）的线性规划问题可以转化为目标函数取极小，转化后的目标函数为： （a ）min z （b ）min(-z) （c ）-min(-z) （d ）-min z （4）运输问题的一般数学模型是一个： （a ）线性规划模型 （b ）混合0-1规划模型 （c ）全0-1规划模型 （d ）混合整数规划模型 （5）．设风险型决策问题中，相应于状态θi 的概率为P(θi )，i=1,2,……,m ；相应于θi 和决策方案d j (j=1,2,……,n)的结局（利润）为u ij ，则完全信息期望值EVPI 等于： (a) ∑∑==?n j ij j i ij n j i j u p u p 11 )(max }{max )(θθ (b) ∑∑==?m i ij i j ij m i j i u p u p 11)(min }{min )(θθ (c) ∑∑==?m i ij i j ij n j i j u p u p 11 )(max }{max )(θθ (d) ∑∑==?m i ij i m i j ij j i u p u p 11)(max }{max )(θθ 三（．（本题满分本题满分20分） 一个工厂用四种原料生产三种产品，生产每种产品要消耗的