SOLUTION: 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 wee

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Question 81512: 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.
Answer by mathdoc316(9) About Me  (Show Source):
You can put this solution on YOUR website!
Here is how to do the word problem part:
First convert the english language in the problem to math language.
I will do this in two steps
The first step is to line up the facts individually like this
Time to produce one AM radio = 15
Time to produce one AM/FM radio = 20
Total production time <= 300
Total radios produced <= 18
Number of AM Radios produced >= 4
Number of AM/FM Radios produced >= 3
The next step is to figure out the variables and constants.
We want to rewrite all the constraints in algebraic terms.
The problem states x is the number of AM radios and y is the number of AM/FM radios.
The last two facts are:
x >= 4
y >= 3
Facts 1 and 2 can be used to translate facts 3 and 4 into math.
"Total radios produced" is x + y
Total production time is:
total time making AM radios
+
total time making AM/FM radios
Total time making AM radios is the number of AM radios multiplied by the amount of time needed to make an AM radio. (Note: In a real factory, employees may not behave in a linear fashion. However an assumption of linearity can be reasonable for a simple model.)
Total time making AM/FM radios is the number of AM/FM radios multiplied by the amount of time needed to make one AM/FM radio.
In math:
Total production time: T+=+15%2Ax+%2B+20%2Ay
Total radios: R+=+x+%2B+y
Now all the constraints are:
1. x >= 4
2. y >= 3
3. x + y <= 18
4. 15 x + 20 y <= 300
Also it is true that x and y are whole numbers.
Also we know x, y, T, and R are all >= 0 so you might want to
graph that too.
I guess you already know how to graph - use the graphing tools on this site if it is a problem. Or ask that part of the question again if that was the part you wanted help with.