SOLUTION: Please help. I am not sure what topic to place the question under I have tried several topics with no results. A small firm produces both AM and AM/FM car radios. The AM radi

Question 113312: Please help. I am not sure what topic to place the question under I have tried several topics with no results.
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 the number of AM/FM radios.
Thanks
JMS
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 the number of AM/FM radios.
----------------------------
Domain and Range:
4<=x<=18
3<=y<=18
------------------
Quantity Inequality:
x+y<=18
--------------------
Production Inequality:
15x + 20y <= 300
-----------------------
Solve Quantity and Production for "y" :
y <= -x+18
y <= (-3/4)x + 15
-------------------------
Graph:
Draw vertical lines at x = 4 and at x = 18
Draw horizontal lines at y = 3 and at y = 18
Note: These limit the domain and the range of the solution set
-------------------------
Graph the boudary lines of the Quantity and production Inequalities:

Darken the area in the feasible solution area that is below both
of these boundary lines.
===============================
Cheers,
Stan H.

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