SOLUTION: I have tried to figure this out and have no idea! I can seperate out some of the information I need, but then I ahve no idea how to orginize it into useable for. Word problems conf

Question 72643This question is from textbook Beginning Algebra
: I have tried to figure this out and have no idea! I can seperate out some of the information I need, but then I ahve no idea how to orginize it into useable for. Word problems confuse me!
A small firm produces both AM and AM/FM car radios. The AM radios take 15h to produce, and the AM/FM radios take 20h. The number of production hours is limited to 300 h per week. The plants capacity is limited to a tatal of 18 radios per week, and existing orders require that at least 4 AM raidos and at least 3 AM/FM radios be produced per week. Write a system of in equalities representing this situation. Then draw a graph of the feasable region given these conditions, in which x is the number of AM radios and y is the number of AM/FM radios. This question is from textbook Beginning Algebra

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A small frim 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 existing 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 is the number of AM/FM radios.
:
Let x = number of AM radios; let y = number of AM/FM radios

The production hour constraint:
15x + 20y =< 300
Arrange in general form to plot the graph
20y =< 300 - 15x
y =< 300/20 - (15/20)x
y =< 15 - .75x, use this to plot the production hr graph (Purple line)
:
Plant's capacity constraint:
x + y =< 18
y =< 18 - x, plot this graph also (Green line)
:
Min AM radio production constraint:
x => 4
This will be a vertical line going thru the x axis at +4, (I can't draw this in)
:
Min AM/FM radio production constaint
y => 3
This will be a horizontal line going thru the y axis at +3, (Dark blue line)
:
Here is the graph as presented by these equations except for x => 4,
:

:
The feasibility region:
1. At or below the purple or green line, whichever is lowest
2. At or above the horizontal line
3. At or to the right of the vertical line which you have to draw in at x = +4
:
How about this, did it all make some sense to you?
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