SOLUTION: A small firm produces both AM and AM?FM car radios. The AM radios take 15 hours to produce and the AM/FM radios take 20 hours. The number of production hours is limited to 300 hour
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Question 36955: A small firm produces both AM and AM?FM car radios. The AM radios take 15 hours to produce and the AM/FM radios take 20 hours. The number of production 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. Answer by mbarugel(146) (Show Source):
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Let's call X to the number of AM radios produced, and Y to the number of AM/FM radios produced. Since X takes 15 hours to produce, and Y takes 20 hours, then total number of hours needed for the whole production must be:
Since total production time can't exceed 300 hours, we get the inequality:
Also, no more than 18 radios can be produced:
Finally, we must produce at least 4 AM radios (X) and at least 3 AM/FM radios (Y). So we get:
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