SOLUTION: Draw the appropriate graphs in the following: A small firm produces both AM and AM/FM car radios. The AM radios take 15 hours to prduce, and the AM/FM radios take 20 hours. The ni

Algebra ->  Graphs -> SOLUTION: Draw the appropriate graphs in the following: A small firm produces both AM and AM/FM car radios. The AM radios take 15 hours to prduce, and the AM/FM radios take 20 hours. The ni      Log On


   

Question 67845: Draw the appropriate graphs in the following:
A small firm produces both AM and AM/FM car radios. The AM radios take 15 hours to prduce, and the AM/FM radios take 20 hours. The nimber of prduction 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. 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.
Any help with this would be greatly appreciated. Thanks.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the appropriate graphs in the following:
A small firm produces both AM and AM/FM car radios.
The AM radios take 15 hours to prduce, and the AM/FM radios take 20 hours.
The nimber of prduction 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.
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Let A be number of AM radios; Let F be number of FM radios.
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Write a system of inequalities representing this situation.
Production Inequality: 15A+20F<=300
Quantity Inequality: A+F<=18
4<=A<=18
3<=F<=18
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Then, draw a graph of the feasible region given these conditions, in which A is the number of AM radios and F is the number of AM/FM radios.
Solve each inequality for F to get:
F<=(-3/4)A+15
F<=-A+18
NOTE: F is the vertical axis; A is the horizontal axis
Draw a vertical line at A=4 and at A=18
Draw a horizontal line at F=3 and F=18
Graph the equality of F<=(-3/4)A+15
Graph the equality of F<=-A+18
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graph%28600%2C400%2C-1%2C25%2C-1%2C25%2C%28-3%2F4%29x%2B15%2C-x%2B18%29
Shade the area that satisfies all the inequalities.
Cheers,
Stan H.