SOLUTION: I am no good with word problems, please help! 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 numbe

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'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.

>>>...require that at least 4 AM radios...be produced per week...<<<

Translation: x is greater than or equal to 4

            x > 4

>>>...require that...at least 3 AM/FM radios be produced per week...<<<

Translation: y is greater than or equal to 3

            y > 3

>>>...The plant's capacity is limited to a total of 18 radios per week...<<

Translation: x and y added together can't be more than 18

        x + y > 18

>>>...The AM radios take 15 h [each] to produce...<<

Translation: to produce x AM radios takes 15x hours

>>>...the AM/FM radios take 20 h [each]...<<<

Translation: to produce y AM/FM radios takes 20y hours.

>>>...The number of production hours is limited to 300 h per week...<<

Translation: 15x hours and 20y hours together must be less than or
             equal to 300 hours

             15x + 20y < 300

We have this system of inequalities:

                     x > 4
                     y > 3
                 x + y > 18
             15x + 20y < 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
          

The feasible region is supposed to be shaded.  I can't do that on here,
but it's the region which is to the right of the vertical line, above
the horizontal line and below both slanted lines.

Edwin