<PRE><B>Question 304905</B>
&lt;pre&gt;&lt;font size = 3&gt;&lt;b&gt;
 7     3    2    1     0     0      5
 4     1    1    0     1     0     20
-5   -10   -1    0     0     1      0

Put in ordinary variables x, y, z, P, 
slack variables s&lt;sub&gt;1&lt;/sub&gt;, s&lt;sub&gt;2&lt;/sub&gt;, and + signs between 
terms where necessary to show addition:  

 7x +  3y + 2z + 1s&lt;sub&gt;1&lt;/sub&gt; + 0s&lt;sub&gt;2&lt;/sub&gt; + 0P =  5
 4x +  1y + 1z + 0s&lt;sub&gt;1&lt;/sub&gt; + 1s&lt;sub&gt;2&lt;/sub&gt; + 0P = 20
-5x - 10y - 1z + 0s&lt;sub&gt;1&lt;/sub&gt; + 0s&lt;sub&gt;2&lt;/sub&gt; + 1P =  0

Erase the terms with 0 coefficients,
and the 1 coefficients:

{{{system(7x + 3y + 2z + s[1]  =  5,
 4x + y + z +  s[2]  = 20,
-5x - 10y - z + P  =  0)}}}

Erase the slack variables in the first two equations
and change the {{{&quot;=&quot;}}} signs to {{{&quot;&quot;&lt;=&quot;&quot;}}}&#39;s. Also, solve
the bottom equation for P

{{{system(7x + 3y + 2z &lt;=  5,
 4x + y + z   &lt;= 20,
P = 5x + 10y + z )}}} 

The problem is:

Maximize {{{P = 5x + 10y + z}}}

subject to the constraints:

{{{system(7x + 3y + 2z &lt;=  5,
 4x + y + z   &lt;= 20, x&gt;=0, y&gt;=0, z&gt;=0)}}}

Edwin&lt;/pre&gt;</PRE>