Question 65561: 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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Production equation: 15x+20y<=300
Quantity equations: x+y<=18
AM radio restrictions: 4<=x<=18
FM radio restrictions: 3<=y<=18
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Solve where you can for y in terms of x:
y<=(-15/20)x+15
y<=-x+18
Cheers,
Stan H.
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