讨论求解:最佳阵容问题的方法

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<p class="MsoNormal" align="center" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center;"><b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt;">B</span></b><b style="mso-bidi-font-weight: normal;"><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt;">题 最佳阵容问题<span lang="EN-US"><p></p></span></span></b></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">有一场由四个项目（高低杠、平衡木、跳马、自由体操）组成的女子体操团体赛，赛程规定：每个<span style="COLOR: red;">队至多允许</span></span><span lang="EN-US" style="COLOR: red; mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 10 </font></span><span style="COLOR: red; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">名运动员参赛</span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">，每一个项目可以有</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 6 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">名选手参加。每个选手参赛的成绩评分从高到低依次为：</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 10 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">；</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 9.9 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">；</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 9.8 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">；</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> … </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">；</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 0.1 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">；</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 0 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">。每个<span style="COLOR: red;">代表队的总分是参赛选手所得总分之和</span>，总分最多的代表队为优胜者。此外，还规定<span style="COLOR: red;">每个运动员只能参加全能比赛</span>（四项全参加）与<span style="COLOR: red;">单项比赛这两类中的一</span>类，参加单项比赛的每个运动员<span style="COLOR: black;">至多只能参加三项单项</span>。每个队应有</span><span style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">
                                <span lang="EN-US" style="COLOR: red;">4 </span></font></span><span style="COLOR: red; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">人参加全能比赛</span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">，其余运动员参加单项比赛。</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">
                                <p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">现某代表队的教练已经对其所带领的</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 10 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">名运动员参加各个项目的成绩进行了大量测试，教练发现每个运动员在每个单项上的成绩稳定在</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 4 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">个得分上（见下表），她们得到这些成绩的相应概率也由统计得出（见表中第二个数据。例如：</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 8.4 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">～</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 0.15 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">表示取得</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 8.4 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">分的概率为</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 0.15 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）。试解答以下问题：</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">
                                <p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、每个选手的各单项得分<span style="COLOR: red;">按最悲观估算</span>，在此前提下，请为该队排出一个出场阵容，使该队<b style="mso-bidi-font-weight: normal;">团体总分尽可能高</b>；每个选手的各单项得分<span style="COLOR: red;">按<b style="mso-bidi-font-weight: normal;">均值估算</b></span>，在此前提下，请为该队排出一个出场阵容，使该队团体总分尽可能高。</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">
                                <p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp;2 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">、若对以往的资料及近期各种信息进行分析得到：本次夺冠的团体总分估计为不少于</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 236.2 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">分，该队为了夺冠应排出怎样的阵容？以该阵容出战，其夺冠前景如何？<span style="COLOR: red;">得分前景（即期望值</span>）又如何？它有</span><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"> 90 </font></span><span style="FONT-FAMILY: 宋体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">％的把握战胜怎样水平的对手？</span></p>

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<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"><p><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">运动员各项目得分及概率分布表贴不上,字数有限制.也可到这儿查看:</span></p></font></span></p><p><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">运动员各项目得分及概率分布表贴不上,字数有限制.也可到这儿查看:</span></p><p></p><p><span lang="EN-US" style="mso-bidi-font-size: 10.5pt;"><font face="Times New Roman"><p><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><a href="http://home.future.org.cn/shumo/problem1.htm"></a></span></p></font></span></p><p><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><a href="http://home.future.org.cn/shumo/problem1.htm"></a></span></p><p></p><span style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;; mso-font-kerning: 1.0pt; mso-bidi-font-family: &quot;Times New Roman&quot;; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;"><a href="http://home.future.org.cn/shumo/problem1.htm">http://home.future.org.cn/shumo/problem1.htm</a></span><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">小弟看到好多学校用这个题做建模模拟比赛题,所以拿来试试,在解第二问时遇到了困难,不知哪位大虾能帮帮忙解释下,那个得分的概率怎么算?</p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;">小弟感激不尽了.</p>

[此贴子已经被作者于2006-8-30 20:58:05编辑过]