6_9.htm

随着各行各业的发展和生产需要

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<p>　</p>
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<table border="1" width="90%">
  <tr>
    <td width="7%">B</td>
    <td width="7%">C<sub>B</sub></td>
    <td width="7%">C<sub>B</sub>B<sup>-1</sup></td>
    <td width="7%">C</td>
    <td width="8%">1</td>
    <td width="8%">2</td>
    <td width="8%">0</td>
    <td width="8%">0</td>
    <td width="8%">0</td>
    <td width="8%">1</td>
    <td width="8%">1</td>
    <td width="8%">1</td>
    <td width="8%">β</td>
  </tr>
  <tr>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">P<sub>0</sub></td>
    <td width="8%">P<sub>1</sub></td>
    <td width="8%">P<sub>2</sub></td>
    <td width="8%">P<sub>3</sub></td>
    <td width="8%">P<sub>4</sub></td>
    <td width="8%">P<sub>5</sub></td>
    <td width="8%">P<sub>6</sub></td>
    <td width="8%">P<sub>7</sub></td>
    <td width="8%">P<sub>8</sub></td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">A<sub>5</sub></td>
    <td width="7%">0</td>
    <td width="7%">0</td>
    <td width="7%">1</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">1</td>
    <td width="8%">1</td>
    <td width="8%">-1</td>
    <td width="8%">-1</td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">A<sub>2</sub></td>
    <td width="7%">0</td>
    <td width="7%">0</td>
    <td width="7%">3/5</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">0</td>
    <td width="8%">-1/5</td>
    <td width="8%">3/5</td>
    <td width="8%">0</td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">A<sub>1</sub></td>
    <td width="7%">0</td>
    <td width="7%">0</td>
    <td width="7%">6/5</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">0</td>
    <td width="8%">3/5</td>
    <td width="8%">-4/5</td>
    <td width="8%">0</td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">w<sub>1</sub>=0</td>
    <td width="7%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">←λ</td>
  </tr>
</table>
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<p>　</p>
<div align="left">

<table border="1" width="90%">
  <tr>
    <td width="7%">B</td>
    <td width="7%">C<sub>B</sub></td>
    <td width="7%">C<sub>B</sub>B<sup>-1</sup></td>
    <td width="7%">C</td>
    <td width="8%">1</td>
    <td width="8%">2</td>
    <td width="8%">0</td>
    <td width="8%">0</td>
    <td width="8%">0</td>
    <td width="8%">1</td>
    <td width="8%">1</td>
    <td width="8%">1</td>
    <td width="8%">β</td>
  </tr>
  <tr>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">P<sub>0</sub></td>
    <td width="8%">P<sub>1</sub></td>
    <td width="8%">P<sub>2</sub></td>
    <td width="8%">P<sub>3</sub></td>
    <td width="8%">P<sub>4</sub></td>
    <td width="8%">P<sub>5</sub></td>
    <td width="8%">P<sub>6</sub></td>
    <td width="8%">P<sub>7</sub></td>
    <td width="8%">P<sub>8</sub></td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">A<sub>5</sub></td>
    <td width="7%">0</td>
    <td width="7%">1/5</td>
    <td width="7%">1</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">1</td>
    <td width="8%">-1</td>
    <td width="8%">-1</td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">A<sub>2</sub></td>
    <td width="7%">2</td>
    <td width="7%">2/5</td>
    <td width="7%">3/5</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">-1/5</td>
    <td width="8%">3/5</td>
    <td width="8%">0</td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">A<sub>1</sub></td>
    <td width="7%">1</td>
    <td width="7%">0</td>
    <td width="7%">6/5</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">3/5</td>
    <td width="8%">-4/5</td>
    <td width="8%">0</td>
    <td width="8%">　</td>
  </tr>
  <tr>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="7%">　</td>
    <td width="8%">0</td>
    <td width="8%">0</td>
    <td width="8%">1/5</td>
    <td width="8%">2/5</td>
    <td width="8%">0</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">　</td>
    <td width="8%">←λ</td>
  </tr>
</table>
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<p>故最优解是y<sub>1</sub>＝6/5 , y<sub>2</sub>＝3/5 , y<sub>3</sub>＝y<sub>4</sub>＝0,y<sub>5</sub>＝1，min 
w<sub>1</sub>＝12/5<br>
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<p>它的对偶问题是：<br>
maxz＝6x<sub>1</sub>＋3x<sub>2</sub>＋2x<sub>3</sub><br>
3x<sub>1</sub>+ x<sub>2</sub> + 2x<sub>3</sub>≤1<br>
4x<sub>1</sub>+ 3x<sub>2</sub> + x<sub>3</sub>≤2<br>
x<sub>1</sub> , x<sub>2</sub> , x<sub>3</sub>≥0<br>
引进松弛变量x<sub>4</sub> , x<sub>5</sub>，单纯形表如下：<br>
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<table border="1" width="85%">
  <tr>
    <td width="10%">B</td>
    <td width="10%">C<sub>B</sub></td>
    <td width="10%">C<sub>B</sub>B<sup>-1</sup></td>
    <td width="10%">C</td>
    <td width="10%">6</td>
    <td width="10%">3</td>
    <td width="10%">2</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">β</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">P<sub>0</sub></td>
    <td width="10%">P<sub>1</sub></td>
    <td width="10%">P<sub>2</sub></td>
    <td width="10%">P<sub>3</sub></td>
    <td width="10%">P<sub>4</sub></td>
    <td width="10%">P<sub>5</sub></td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>4</sub></td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">1</td>
    <td width="10%">3</td>
    <td width="10%">(1)</td>
    <td width="10%">2</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">1/3</td>
  </tr>
  <tr>
    <td width="10%">A<sub>5</sub></td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">2</td>
    <td width="10%">4</td>
    <td width="10%">3</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">1</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">z'=0</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">6</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">←λ</td>
  </tr>
</table>
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<p>　</p>
<div align="left">

<table border="1" width="85%">
  <tr>
    <td width="10%">B</td>
    <td width="10%">C<sub>B</sub></td>
    <td width="10%">C<sub>B</sub>B<sup>-1</sup></td>
    <td width="10%">C</td>
    <td width="10%">6</td>
    <td width="10%">3</td>
    <td width="10%">2</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">β</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">P<sub>0</sub></td>
    <td width="10%">P<sub>1</sub></td>
    <td width="10%">P<sub>2</sub></td>
    <td width="10%">P<sub>3</sub></td>
    <td width="10%">P<sub>4</sub></td>
    <td width="10%">P<sub>5</sub></td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>1</sub></td>
    <td width="10%">6</td>
    <td width="10%">2</td>
    <td width="10%">1/3</td>
    <td width="10%">1</td>
    <td width="10%">1/3</td>
    <td width="10%">　</td>
    <td width="10%">1/3</td>
    <td width="10%">0</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>5</sub></td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">2/3</td>
    <td width="10%">0</td>
    <td width="10%">(5/3)</td>
    <td width="10%">　</td>
    <td width="10%">-4/3</td>
    <td width="10%">1</td>
    <td width="10%">2/5</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">z'=2</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">1</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">←λ</td>
  </tr>
</table>
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<p>　</p>
<div align="left">

<table border="1" width="85%">
  <tr>
    <td width="10%">B</td>
    <td width="10%">C<sub>B</sub></td>
    <td width="10%">C<sub>B</sub>B<sup>-1</sup></td>
    <td width="10%">C</td>
    <td width="10%">6</td>
    <td width="10%">3</td>
    <td width="10%">2</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">β</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">P<sub>0</sub></td>
    <td width="10%">P<sub>1</sub></td>
    <td width="10%">P<sub>2</sub></td>
    <td width="10%">P<sub>3</sub></td>
    <td width="10%">P<sub>4</sub></td>
    <td width="10%">P<sub>5</sub></td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>1</sub></td>
    <td width="10%">6</td>
    <td width="10%">6/5</td>
    <td width="10%">1/5</td>
    <td width="10%">　</td>
    <td width="10%">1</td>
    <td width="10%">　</td>
    <td width="10%">3/5</td>
    <td width="10%">-1/5</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>2</sub></td>
    <td width="10%">3</td>
    <td width="10%">3/5</td>
    <td width="10%">2/5</td>
    <td width="10%">　</td>
    <td width="10%">1</td>
    <td width="10%">　</td>
    <td width="10%">-4/5</td>
    <td width="10%">3/5</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">　</td>
    <td width="10%">z'=12/5</td>
    <td width="10%">　</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">-1</td>
    <td width="10%">-6/5</td>
    <td width="10%">-3/5</td>
    <td width="10%">←λ</td>
  </tr>
</table>
</div>

<p>故最优解是y<sub>1</sub>= 6/5，y<sub>2</sub>＝3/5, min w= 12/5<br>
</p>
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