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< >需要选购一些规格固定的降落伞向灾区空投救灾物质，空投高度<FONT face="Times New Roman">500m</FONT>，救灾物质落地的速度不能超过<FONT face="Times New Roman">20m/s</FONT>。知道降落伞面是半径为<FONT face="Times New Roman">r</FONT>的半球面，每个降落伞都有<FONT face="Times New Roman">16</FONT>根相同长度<FONT face="Times New Roman">L</FONT>的绳索。每个降落伞的制造费用固定为<FONT face="Times New Roman">200</FONT>元，绳索价格<FONT face="Times New Roman">4</FONT>元<FONT face="Times New Roman">/m</FONT>，降落伞面费用见表<FONT face="Times New Roman">1</FONT>。<p></p></P>
< >降落伞在降落过程中受到的空气阻力与降落速度以及伞面积成正比。用半径<FONT face="Times New Roman">r=3m</FONT>、载重<FONT face="Times New Roman">300kg</FONT>的降落伞从<FONT face="Times New Roman">500m</FONT>高度降落，得到一些数据如表<FONT face="Times New Roman">2</FONT>。<p></p></P>
< >要求：<p></p></P>
<P ><FONT face="Times New Roman">1</FONT>、当救灾物质共<FONT face="Times New Roman">2000kg</FONT>时，确定降落伞的选购方案，使购买费用尽可能少？<p></p></P>
<P ><FONT face="Times New Roman">2</FONT>、当救灾物质不能被随意连续分割时，为使购买费用尽可能少建立数学模型，并对表<FONT face="Times New Roman">3</FONT>数据给出结果。<p></p></P>
<P >表<FONT face="Times New Roman">1<p></p></FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">r</FONT>（<FONT face="Times New Roman">m</FONT>）<p></p></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">2<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">2.5<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">3<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">3.5<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">4<p></p></FONT></P></TD></TR>
<TR>
<TD  vAlign=top width=89>
<P  align=center>费用（元）<p></p></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">65<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">170<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">350<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">660<p></p></FONT></P></TD>
<TD  vAlign=top width=89>
<P  align=center><FONT face="Times New Roman">1000<p></p></FONT></P></TD></TR></TABLE>
<P >表<FONT face="Times New Roman">2<p></p></FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR>
<TD  vAlign=top width=114>
<P  align=center>时刻<FONT face="Times New Roman">t</FONT>（<FONT face="Times New Roman">s</FONT>）<p></p></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">0<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">3<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">6<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">9<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">12<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">15<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">18<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">21<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">24<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">27<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">30<p></p></FONT></P></TD></TR>
<TR>
<TD  vAlign=top width=114>
<P  align=center>高度<FONT face="Times New Roman">h</FONT>（<FONT face="Times New Roman">m</FONT>）<p></p></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">500<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">470<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">425<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">372<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">317<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">264<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">215<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">160<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">108<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">55<p></p></FONT></P></TD>
<TD  vAlign=top width=38>
<P  align=center><FONT face="Times New Roman">1<p></p></FONT></P></TD></TR></TABLE>
<P >表<FONT face="Times New Roman">3<p></p></FONT></P>
<TABLE  cellSpacing=0 cellPadding=0 border=1>

<TR>
<TD  vAlign=top width=115>
<P  align=center>物质规格（<FONT face="Times New Roman">kg</FONT>）<p></p></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">2<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">3<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">5<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">18<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">24<p></p></FONT></P></TD></TR>
<TR>
<TD  vAlign=top width=115>
<P  align=center>数量（个）<p></p></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">40<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">30<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">30<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">25<p></p></FONT></P></TD>
<TD  vAlign=top width=82>
<P  align=center><FONT face="Times New Roman">12<p></p></FONT></P></TD></TR></TABLE>

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