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IsTim

  • 2 years ago

The total cost, C, in dollars, of operating a factory that produces kitchen utensils is (x)=0.5x^2+40x+8000, where x is the number of items produced, in thousands. Determine the rate of change of the average cost of producing 5000 times. Interpret this value.

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  1. IsTim
    • 2 years ago
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    No work done.

  2. IsTim
    • 2 years ago
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    Average cost is $1.64.

  3. tiaph
    • 2 years ago
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    Woah. This is something different. Hmm. when u say average cost is 1.64 meaning that is part of the questions. or u worked it out?

  4. IsTim
    • 2 years ago
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    Worked it out.

  5. IsTim
    • 2 years ago
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    I did this from dividing the total cost by the number of items produced.

  6. tiaph
    • 2 years ago
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    Hmm i think this questions has a bit of problem in it. Cause it asks for the rate of change of the cost of producing 5000 items. That means you have to take into account the time taken to produce 1 item, which you cannot find given the limited information given in the question. Note: Rate always involves time. So now i have not a clue what the question really wants. Cant really help =x

  7. IsTim
    • 2 years ago
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    I have determined the marginal cost of producing 50000 items, and cost of producing 5001st item. Would that help? The rate is also related to the derivative, if that helps with anything. Actually, This have given me a iddea. With the Cost function's derivative help?

  8. tiaph
    • 2 years ago
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    Okay looking at your reply i got an idea too. First i stand by my point, using the term 'rate' here is wrong and just serve to confuse. WHat i think the question is getting at is the marginal cost of producing one more item in addition to the 5000 items.

  9. IsTim
    • 2 years ago
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    Whoops, 5000, not 50 000

  10. tiaph
    • 2 years ago
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    Given (x)=0.5x^2+40x+8000. as the formula for total cost. By differentiating it, you will get the marginal costs Marginal cost, MC = x+40 Substitute x = 5, (Note the questions state that x is the number of items produced in thousands, so is 5 instead of 5000) MC = 5+40 =$45 intepreting it in words, $45 is the additional cost of producing the 5000st unit.

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