露天矿井和粮库选址的问题,请大侠们帮忙指点一下拉!!!!!

冬夏卡卡

<H3  align=center>露天采矿问题（<FONT face="Times New Roman">A</FONT>）<p></p></H3>
< >某公司获准在一块<v:shapetype><FONT face="Times New Roman"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></FONT></v:shapetype><v:shape><v:imagedata>200米*200米</v:imagedata></v:shape>的方形土地上露天采矿。因为土石滑坡，挖坑的坑边坡度不能超过<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>。公司已得到不同位置不同深度处的矿砂所含纯金属的百分数的估计值。考虑到坡角对挖坑工作所加的限制，公司决定将问题按长方形块的挖取问题处理。</P>
< >每个长方形块的水平尺寸为<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>，铅直尺寸为<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>。若在一个深度层上挖了<FONT face="Times New Roman">4</FONT>块；则在下一层上还可为挖一块；下图所示的情形（实线为上一层块，虚线为下一层块）是俯视这<FONT face="Times New Roman">5</FONT>块的水平位置关系。</P>
< ><v:shape><v:imagedata></v:imagedata></v:shape><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P><BR  clear=all>
<P ><FONT size=2>俯视图</FONT></P>
<P >这样以来，所能挖取的块数，第一层最多<FONT face="Times New Roman">16</FONT>块，第二层最多<FONT face="Times New Roman">9</FONT>块，第三层最多<FONT face="Times New Roman">4</FONT>块，第四层最多<FONT face="Times New Roman">1</FONT>块。不能再往深挖取。所有这些可能挖取的块，按已得的估计值，将各块含金属的百分数作为块的值，则各块的值如下：</P>
<P ><FONT size=2>第一层（地表层）</FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR >
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.5</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.5</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.5</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.75</FONT></P></TD></TR>
<TR >
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.5</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>2.0</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.5</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.75</FONT></P></TD></TR>
<TR >
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.0</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>1.0</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.75</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.5</FONT></P></TD></TR>
<TR >
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.75</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.75</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.5</FONT></P></TD>
<TD  width=115>
<P ><FONT face="Times New Roman" size=2>0.25</FONT></P></TD></TR></TABLE>
<P ><FONT size=2>第二层（深<FONT face="Times New Roman">25m</FONT>处）</FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR >
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>4.0</FONT></P></TD>
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>4.0</FONT></P></TD>
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>2.0</FONT></P></TD></TR>
<TR >
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>3.0</FONT></P></TD>
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>3.0</FONT></P></TD>
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>1.0</FONT></P></TD></TR>
<TR >
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>2.0</FONT></P></TD>
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>2.0</FONT></P></TD>
<TD  width=116>
<P ><FONT face="Times New Roman" size=2>0.5</FONT></P></TD></TR></TABLE>
<P ><FONT size=2>第三层（深<FONT face="Times New Roman">50m</FONT>处）</FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR >
<TD  vAlign=top width=118>
<P ><FONT face="Times New Roman" size=2>12.0</FONT></P></TD>
<TD  vAlign=top width=118>
<P ><FONT face="Times New Roman" size=2>6.0</FONT></P></TD></TR>
<TR >
<TD  vAlign=top width=118>
<P ><FONT size=2><FONT face="Times New Roman"> 5.0</FONT></FONT></P></TD>
<TD  vAlign=top width=118>
<P ><FONT face="Times New Roman" size=2>4.0</FONT></P></TD></TR></TABLE>
<P ><FONT size=2><FONT face="Times New Roman">        </FONT>第四层（深<FONT face="Times New Roman">75m</FONT>处）</FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR >
<TD  width=125>
<P ><FONT face="Times New Roman" size=2>6.0</FONT></P></TD></TR></TABLE>
<P ><FONT size=2>各层的块挖取费用</FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR >
<TD  width=92>
<P  align=center>层<p></p></P></TD>
<TD  width=92>
<P  align=center><FONT size=2>一</FONT></P></TD>
<TD  width=92>
<P  align=center><FONT size=2>二</FONT></P></TD>
<TD  width=92>
<P  align=center><FONT size=2>三</FONT></P></TD>
<TD  width=92>
<P  align=center><FONT size=2>四</FONT></P></TD></TR>
<TR >
<TD  width=92>
<P  align=center>块费用<p></p></P></TD>
<TD  width=92>
<P  align=center><FONT face="Times New Roman" size=2>3000</FONT></P></TD>
<TD  width=92>
<P  align=center><FONT face="Times New Roman" size=2>6000</FONT></P></TD>
<TD  width=92>
<P  align=center><FONT face="Times New Roman" size=2>8000</FONT></P></TD>
<TD  width=92>
<P  align=center><FONT face="Times New Roman" size=2>10000</FONT></P></TD></TR></TABLE>
<P >挖取一块的收入同该块值成正比；挖一个值为<FONT face="Times New Roman">100</FONT>的块可收入为<FONT face="Times New Roman">200000</FONT>。试建立一模型以帮助决定挖取哪些块，使纯收入最大。</P>
<H3  align=center>粮库选址问题（<FONT face="Times New Roman">B</FONT>）<p></p></H3>
<P >某乡要建立一个粮库，以存储各村农民上缴的公粮。该乡九个村庄<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>，如下图所示：</P>
<P ><v:group><v:group><v:group><v:group><v:group><v:group><v:group><v:group><v:group><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:group><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line><v:line><v:stroke endarrow="oval" startarrow="oval"></v:stroke></v:line></v:group></v:group></v:group></v:group></v:group></v:group></v:group></v:group></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1055">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">A-50<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1056">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">B-70<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1057">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">C-60<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1058">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">D-20<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1059">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">E-80<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1060">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">F-20<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1061">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">G-70<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1062">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">H-30<p></p></FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><v:rect><v:textbox style="mso-next-textbox: #_x0000_s1063">
<TABLE cellSpacing=0 cellPadding=0 width="100%">

<TR>
<TD >
<DIV>
<P ><FONT face="Times New Roman">I-50</FONT></P></DIV></TD></TR></TABLE></v:textbox></v:rect></v:group><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
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<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P><BR  clear=all>
<P >图中的数字是各村要上交的公粮数（吨），各村之间的距离为：<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>，<v:shape> <v:imagedata></v:imagedata></v:shape>。</P>
<P >为了最大限度地减少运输费用，粮库就应建在合适的位置（或在村中，或在村间的道路上）。试建立一模型以确定粮库的最佳位置。</P>