Question 65645: Draw the appropriate graphs in each of the following.
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 4AM 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 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 4AM 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.
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Let number of AM radios be "a": Hours to produce = 15a hours
Let number of FM radios be "f": Hours to produce is 20f hours
a+f<=18
4<=a<=18
3<=f<=18
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Solve for f: f<=-a+18
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Graph the equality and the half-plane below it.
Draw vertical lines at a=4 and a=18
Draw horizontal lines at f=3 and f=18
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Cheers,
Stan H.
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