<PRE><B>Question 51388</B>
&lt;pre&gt;&lt;font size = 3&gt;&lt;b&gt;
A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to
produce, and the AM/FM radios take 20 h. The number of production hours is
limited to 300 h per week. The plant&#39;s capacity is limited to a total of 18
radios per week, and exisitng orders require that at least 4 AM radios and at
least 3 AM/FM radios be produced per week. Write a system of inequalities
representing this situation. Then draw a graph of the feasible region given
these conditions, in which x is the number of AM radios and y the number of
AM/FM radios.

&gt;&gt;&gt;...require that at least 4 AM radios...be produced per week...&lt;&lt;&lt;

Translation: x is greater than or equal to 4

            x &lt;u&gt;&gt;&lt;/u&gt; 4

&gt;&gt;&gt;...require that...at least 3 AM/FM radios be produced per week...&lt;&lt;&lt;

Translation: y is greater than or equal to 3

            y &lt;u&gt;&gt;&lt;/u&gt; 3

&gt;&gt;&gt;...The plant&#39;s capacity is limited to a total of 18 radios per week...&lt;&lt;

Translation: x and y added together can&#39;t be more than 18

        x + y &lt;u&gt;&gt;&lt;/u&gt; 18

&gt;&gt;&gt;...The AM radios take 15 h [each] to produce...&lt;&lt;

Translation: to produce x AM radios takes 15x hours

&gt;&gt;&gt;...the AM/FM radios take 20 h [each]...&lt;&lt;&lt;

Translation: to produce y AM/FM radios takes 20y hours.

&gt;&gt;&gt;...The number of production hours is limited to 300 h per week...&lt;&lt;

Translation: 15x hours and 20y hours together must be less than or
             equal to 300 hours

             15x + 20y &lt;u&gt;&lt;&lt;/u&gt; 300

We have this system of inequalities:

                     x &lt;u&gt;&gt;&lt;/u&gt; 4
                     y &lt;u&gt;&gt;&lt;/u&gt; 3
                 x + y &lt;u&gt;&gt;&lt;/u&gt; 18
             15x + 20y &lt;u&gt;&lt;&lt;/u&gt; 300

We now graph the four boundary lines whose equations are the
above inequalities with equal signs replacing to inequality
signs.

                     x = 4
                     y = 3
                 x + y = 18
             15x + 20y = 300

x = 4 is a vertical line 4 units right of the y-axis
y = 3 is a horixontal line 3 units above the x-axis
x + y = 18 has intercepts (18, 0) and (0, 18)
15x + 20y = 300 has intercepts (20, 0) and (0, 15)

Draw the 4 lines
          {{{ graph( 300, 300, -2, 25, -2, 25, 999(x-4), 3, 18-x, (300-15x)/20) }}}

The feasible region is supposed to be shaded.  I can&#39;t do that on here,
but it&#39;s the region which is to the right of the vertical line, above
the horizontal line and below both slanted lines.

Edwin&lt;/pre&gt;
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