有谁参加上海市中学生应用数学夏令营

MCM王子

该用什么方法做？

MCM王子

< 0cm 0cm 0pt; TEXT-INDENT: 21pt; mso-char-indent-count: 2.0; mso-char-indent-size: 10.5pt">某机械厂一车间有<FONT face="Times New Roman">A,B,C</FONT>三种产品。假设生产每件所需工人，工时及估计利润由下表给出：</P>
<TABLE medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt" cellSpacing=0 cellPadding=0 border=1>

<TR>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 0.5pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" vAlign=top width=81 rowSpan=2>
< 0cm 0cm 0pt">产品</P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 0.5pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 243.45pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt" vAlign=top width=325 colSpan=4>
< 0cm 0cm 0pt">所需工人</P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 0.5pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt" vAlign=top width=81 rowSpan=2>
<P 0cm 0cm 0pt">工时</P>
<P 0cm 0cm 0pt">天<FONT face="Times New Roman">/</FONT>件</P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 0.5pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt" vAlign=top width=81 rowSpan=2>
<P 0cm 0cm 0pt">利润</P>
<P 0cm 0cm 0pt">万元<FONT face="Times New Roman">/</FONT>件</P></TD></TR>
<TR>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt">技术工人</P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt">普通工人</P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt">辅助工人</P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt">机械师</P></TD></TR>
<TR>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">A</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">3</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">4</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">2</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">1</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">2</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">3.5</FONT></P></TD></TR>
<TR>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">B</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">2</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">3</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">2</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">1</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">1</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">2.2</FONT></P></TD></TR>
<TR>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">C</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">0</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">4</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.85pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">1</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">1</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">0.2</FONT></P></TD>
<TD windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #d4d0c8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #d4d0c8; WIDTH: 60.9pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=81>
<P 0cm 0cm 0pt"><FONT face="Times New Roman">0.2</FONT></P></TD></TR></TABLE>
<P 0cm 0cm 0pt">车间里现有技术工人阶级<FONT face="Times New Roman">21</FONT>名，普通工人<FONT face="Times New Roman">60</FONT>名，辅助工人<FONT face="Times New Roman">30</FONT>名，机械师<FONT face="Times New Roman">16</FONT>名（注：若有空闲，技术工人可干普通工人或辅助工人的工作，普通工人也可以充任辅助工人。但机械师工作其它人不能胜任。）</P>
<P 0cm 0cm 0pt 56.25pt; TEXT-INDENT: -35.25pt; mso-list: l0 level1 lfo1; tab-stops: list 56.25pt"><FONT face="Times New Roman">1．<FONT size=3>             </FONT></FONT>若不考虑市场对产品的需求，试设计能使总利润最大的月度计划（以每月<FONT face="Times New Roman">22</FONT>工作日计）；</P>
<P 0cm 0cm 0pt 56.25pt; TEXT-INDENT: -35.25pt; mso-list: l0 level1 lfo1; tab-stops: list 56.25pt"><FONT face="Times New Roman">2．<FONT size=3>             </FONT></FONT>最近国家规定：这三种产品的外表必须喷涂某种环保漆。<FONT face="Times New Roman">A,B,C</FONT>三种产品每种使用的该环保漆的数量分别为此<FONT face="Times New Roman">300g</FONT>，<FONT face="Times New Roman">100g</FONT>，<FONT face="Times New Roman">400g.</FONT>由于该种环保漆的供应不正常，厂方既要求总利润最大，又要求使用的环保漆总量尽可能少，此时应如何设计生产计划？</P>3．若三种产品的月度需求量满足参数分别为λ1=15、λ2=80、λ3=80的Poisson分布，从考虑社会效益和工厂利润的角度出发，应如何制定生产计划。

frankcds2002

<>[em01]</P>
<>1.线性优化问题：利润最大，可以看一些运筹学的书</P>
<>2.多目标优化 ：可以化简成单目标优化</P>
<P>3.结合一、二，可以获取最优</P>