< ><FONT face=宋体 color=#808080 size=4>武汉理工大学2004年数学建模精英挑战赛试题</FONT></P>
<><B normal?><FONT face="Times New Roman">A </FONT></B><B normal?>题</B><B normal?>
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< 0cm 0pt?><B normal?><FONT face="Times New Roman"> </FONT></B><B normal?>草原命运</B><B normal?>
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<P LINE-HEIGHT: 0pt; 0cm 200%?><FONT face="Times New Roman"> </FONT>天然草原的生息繁衍<FONT face="Times New Roman">,</FONT>已形成自身特有的生物链<FONT face="Times New Roman">,</FONT>且对人类生存起着重要作用。长期以来<FONT face="Times New Roman">,</FONT>人为破坏<FONT face="Times New Roman">(</FONT>如过度放牧、猎杀动物及采挖草药等<FONT face="Times New Roman">)</FONT>使草原生态每况愈下<FONT face="Times New Roman">,</FONT>日渐衰竭。据<FONT face="Times New Roman">2000</FONT>年<FONT face="Times New Roman">8</FONT>月<FONT face="Times New Roman">6</FONT>日《北京晚报》载<FONT face="Times New Roman">:</FONT>“……受利益驱使<FONT face="Times New Roman">,</FONT>有些人不顾国家法律和当地政府禁令<FONT face="Times New Roman">,</FONT>在呼伦贝尔草原大肆采挖中草药<FONT face="Times New Roman">,</FONT>致使草原严重受损。据此<FONT face="Times New Roman">,</FONT>有关专家推断<FONT face="Times New Roman">,10</FONT>年之内<FONT face="Times New Roman">,</FONT>该草原将变成荒漠。”为了天然草原的生息繁衍和可持续发展<FONT face="Times New Roman">,</FONT>完成以下工作<FONT face="Times New Roman">:
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<P LINE-HEIGHT: 0pt; 0cm 200%?><FONT face="Times New Roman"> 1)</FONT>建立草原自然生长规律模型<FONT face="Times New Roman">,</FONT>描述人为破坏对草原生长的影响过程<FONT face="Times New Roman">;(
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<P LINE-HEIGHT: 0pt; 0cm 200%?><FONT face="Times New Roman"> 2)</FONT>论证或驳斥报载消息中专家的推断<FONT face="Times New Roman">,</FONT>如果立即停止对草原的一切人为破坏<FONT face="Times New Roman">,10</FONT>年后的情形如何<FONT face="Times New Roman">?
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<P LINE-HEIGHT: 0pt; 0cm 200%?><FONT face="Times New Roman"> 3)</FONT>寻求导致草原消失的临界条件<FONT face="Times New Roman">,</FONT>给出草原生长的挽救方案<FONT face="Times New Roman">,</FONT>并对挽救效果进行预测。
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<P><FONT face="Times New Roman"></FONT></P><B normal?><FONT face="Times New Roman">B</FONT></B><B normal?>题</B>
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<P LINE-HEIGHT: 0pt; 0cm 200%?><B normal?> </B><B normal?>最佳培养基配比方案</B><B normal?>
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<P 21pt; TEXT-INDENT: LINE-HEIGHT: 0pt; 0cm 200%?>以下是某发酵实验中培养基的碳源<FONT face="Times New Roman">(C1,C2,C3)</FONT>和氮源<FONT face="Times New Roman">(N1,N2,N3,N4)</FONT>含量及<FONT face="Times New Roman">IFN-</FONT>γ<FONT face="Times New Roman">(</FONT>γ<FONT face="Times New Roman">-</FONT>干扰素<FONT face="Times New Roman">)</FONT>的产量的实验数据表<FONT face="Times New Roman">(</FONT>见表<FONT face="Times New Roman">1),</FONT>如何选择碳源和氮源的种类及含量使<FONT face="Times New Roman">IFN-</FONT>γ的产量达到最大<FONT face="Times New Roman">?</FONT>试建立数学模型<FONT face="Times New Roman">,</FONT>给出培养基的最优配比方案。表<FONT face="Times New Roman">1</FONT> 培养基实验数据表
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<P 21pt; TEXT-INDENT: LINE-HEIGHT: 0pt; 0cm 200%?>
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<P mso-char-indent-count: TEXT-INDENT: LINE-HEIGHT: 0pt; 0cm 11.06? 200%; 133.25pt;><B normal?>表</B><B normal?><FONT face="Times New Roman">1
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<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">NO. C<st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="True" SourceValue="1" UnitName="C">1 C</st1:chmetcnv><st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="True" SourceValue="2" UnitName="C">2 C</st1:chmetcnv>3 N1 N2 N3 N4 rhIFN-</FONT>γ</P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">1 0.1 0 0 0 0.5 0 0 11.6900</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">2 0.4 0 0 0 0.5 0 0 39.1297</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">3 1 0 0 0 0.5 0 0 68.2035</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">4 2 0 0 0 0.5 0 0 83.6580</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">5 3 0 0 0 0.5 0 0 75.4200</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">6 0 0.2 0 0 0.5 0 0 20.7360</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">7 0 0.5 0 0 0.5 0 0 20.7417</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">8 0 0.8 0 0 0.5 0 0 22.5836</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">9 0 1.5 0 0 0.5 0 0 25.8213</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">10 0 0 0.1 0 0.5 0 0 5.6240</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">11 0 0 0.5 0 0.5 0 0 10.2357</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">12 0 0 1.5 0 0.5 0 0 14.5909</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">13 0 0 2.5 0 0.5 0 0 20.3346</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">14 0 0 0 0 0.5 0 0 7.2960</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">15 0 0 0 0 0.5 0 0 42.5880</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">16 0 0 0 0 0.5 0 0 51.6000</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">17 2 0 0 0 0 0 0 165.5400</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">18 2 0 0 0.5 0 0 0 72.0000</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">19 2 0 0 2 0 0 0 54.9000</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">20 2 0 0 3 0 0 0 42.8400</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">21 2 0 0 4 0 0 0 164.2500</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">22 2 0 0 5 0 0 0 138.0400</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">23 2 0 0 0 0 0 0 126.9000</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">24 2 0 0 0 0.5 0.5 0 11.4840</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">25 2 0 0 0 2 2 0 17.1600</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">26 2 0 0 0 3 3 0 20.8000</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">27 2 0 0 0 4 4 0 57.2400</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">28 2 0 0 0 5 5 0 72.9600</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">29 2 0 0 0 0 0 0.01 17.6080</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">30 2 0 0 0 0 0 0.05 30.9400</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">31 2 0 0 0 0 0 0.1 11.4750</FONT></P>
<P mso-char-indent-count: TEXT-INDENT: 0pt; 0cm .5? 5.25pt;><FONT face="Times New Roman">32 2 0 0 0 0 0 0.3 12.0840</FONT></P> |
发表于 2004-5-7 07:58:08