SOLUTION: I need some help with the following word problem... A small firm produces both AM and AM/FM ca radios. The AM radios take 15 hours to produce, and the AM/FM radios take 20 hours

Question 148701: I need some help with the following word problem...
A small firm produces both AM and AM/FM ca radios. The AM radios take 15 hours to produce, and the AM/FM radios take 20 hours to produce. The Number of production hours is limited to 300 hours 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. In this case let x= AM Radios and y= AM/FM radios.
Would it be 15x + 20y (less than or equal to) 300 ???
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
This same problem came up a few weeks ago. This is what I submitted then. Perhaps it will help you

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 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
::
Min AM/FM radio production constraint
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
:
How about this, did it all make some sense to you?
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