6_5.htm

随着各行各业的发展和生产需要

    <td width="11%">-2</td>
    <td width="12%">←λ</td>
  </tr>
</table>

<p>　</p>

<table border="1" width="75%">
  <tr>
    <td width="11%">B</td>
    <td width="11%">C<sub>B</sub></td>
    <td width="11%">C→</td>
    <td width="11%">3</td>
    <td width="11%">6</td>
    <td width="11%">2</td>
    <td width="11%">0</td>
    <td width="11%">0</td>
    <td width="12%">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </td>
  </tr>
  <tr>
    <td width="11%">　</td>
    <td width="11%">　</td>
    <td width="11%">P<sub>0</sub></td>
    <td width="11%">P<sub>1</sub></td>
    <td width="11%">P<sub>2</sub></td>
    <td width="11%"><p align="left">P<sub>3</sub></td>
    <td width="11%"><p align="left">P<sub>4</sub></td>
    <td width="11%"><p align="left">P<sub>5</sub></td>
    <td width="12%">　</td>
  </tr>
  <tr>
    <td width="11%"><p align="left">A<sub>1</sub></td>
    <td width="11%">3</td>
    <td width="11%">2/5</td>
    <td width="11%">1</td>
    <td width="11%">0</td>
    <td width="11%">-1</td>
    <td width="11%">3/5&nbsp; </td>
    <td width="11%">-4/5</td>
    <td width="12%">　</td>
  </tr>
  <tr>
    <td width="11%">A<sub>2</sub></td>
    <td width="11%">6</td>
    <td width="11%">1/5</td>
    <td width="11%">0</td>
    <td width="11%">1</td>
    <td width="11%">1</td>
    <td width="11%">-1/5</td>
    <td width="11%">3/5</td>
    <td width="12%">　</td>
  </tr>
  <tr>
    <td width="11%">　</td>
    <td width="11%">z=12/5</td>
    <td width="11%">　</td>
    <td width="11%">0</td>
    <td width="11%">0</td>
    <td width="11%">-1</td>
    <td width="11%"><p align="left">-3/5</td>
    <td width="11%">-6/5</td>
    <td width="12%">←λ</td>
  </tr>
</table>

<p>　</p>

<p>故最优解为x<sub>1</sub>=2/5,x<sub>2</sub>=1/5,目标函数z=12/5.</p>

<p><b>例２</b>　maxz＝x<sub>1</sub>+2x<sub>5</sub>－x<sub>6</sub>，</p>

<p>－(12/7)x<sub>1</sub>+(1/14)x<sub>2</sub>+(5/14)x<sub>3</sub>+x<sub>4</sub>＝45/7</p>

<p>(1/7)x<sub>1</sub>－(3/14)x<sub>2</sub>－(1/14)x<sub>3</sub>+x<sub>5</sub>＝5/7</p>

<p>－(3/7)x<sub>1</sub>+(1/7)x<sub>2</sub>－(2/7)x<sub>3</sub>+x<sub>6</sub>＝6/7 </p>

<p>x<sub>1</sub>，…，x<sub>6</sub>≥0． </p>

<p>问题的单纯形表如下：　</p>
<div align="left">

<table border="1" width="85%">
  <tr>
    <td width="11%">B</td>
    <td width="11%">C<sub>B</sub></td>
    <td width="11%">C→</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">2</td>
    <td width="10%">-1</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <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%">P<sub>6</sub></td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>4</sub></td>
    <td width="10%">0</td>
    <td width="10%">45/7</td>
    <td width="10%">-12/7</td>
    <td width="10%">1/14</td>
    <td width="10%">5/14</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">90</td>
  </tr>
  <tr>
    <td width="10%">A<sub>5</sub></td>
    <td width="10%">2</td>
    <td width="10%">5/7</td>
    <td width="10%">1/7</td>
    <td width="10%">-3/14</td>
    <td width="10%">-1/14</td>
    <td width="10%">0</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>6</sub></td>
    <td width="10%">-1</td>
    <td width="10%">6/7</td>
    <td width="10%">-3/7</td>
    <td width="10%">(1/7)</td>
    <td width="10%">-2/7</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">1</td>
    <td width="10%">(6)</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">z=4/7</td>
    <td width="10%">　</td>
    <td width="10%">2/7</td>
    <td width="10%">4/7</td>
    <td width="10%">-1/7</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">←λ</td>
  </tr>
</table>
</div>

<p>　</p>
<div align="left">

<table border="1" width="85%">
  <tr>
    <td width="11%">B</td>
    <td width="11%">C<sub>B</sub></td>
    <td width="11%">C→</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">2</td>
    <td width="10%">-1</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <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%">P<sub>6</sub></td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>4</sub></td>
    <td width="10%">0</td>
    <td width="10%">6</td>
    <td width="10%">-3/2</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">1/2</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">-1/2</td>
  </tr>
  <tr>
    <td width="10%">A<sub>5</sub></td>
    <td width="10%">2</td>
    <td width="10%">2</td>
    <td width="10%">-1/2</td>
    <td width="10%">0</td>
    <td width="10%">-1/2</td>
    <td width="10%">0</td>
    <td width="10%">1</td>
    <td width="10%">3/2</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">A<sub>2</sub></td>
    <td width="10%">0</td>
    <td width="10%">6</td>
    <td width="10%">-3</td>
    <td width="10%">1</td>
    <td width="10%">-2</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">7</td>
    <td width="10%">　</td>
  </tr>
  <tr>
    <td width="10%">　</td>
    <td width="10%">z=4</td>
    <td width="10%">　</td>
    <td width="10%">2</td>
    <td width="10%">0</td>
    <td width="10%">1</td>
    <td width="10%">0</td>
    <td width="10%">0</td>
    <td width="10%">-4</td>
    <td width="10%">←λ</td>
  </tr>
</table>
</div>

<p>由于c<sub>1</sub>－z<sub>1</sub>＞0，但P<sub>1</sub>＝( －3/2 , －1/2, －3)<sup>T</sup>,所有元素都为负数，故问题无解．</p>

<p><img src="6_5_7.gif"></p>
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