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mathcalculus Group Title

FIND: The minimal average cost (ATTACHED.)

  • 11 months ago
  • 11 months ago

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  1. mathcalculus Group Title
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    • 11 months ago
  2. satellite73 Group Title
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    minimum is at the vertex compute \(-\frac{b}{2a}\) with \(b=700,a=1\)

    • 11 months ago
  3. satellite73 Group Title
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    oh, i see you did that. hmmmm

    • 11 months ago
  4. satellite73 Group Title
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    weird i guess to minimize the cost, produce nothing

    • 11 months ago
  5. mathcalculus Group Title
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    ?

    • 11 months ago
  6. mathcalculus Group Title
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    i understood part d.... it's 280

    • 11 months ago
  7. satellite73 Group Title
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    you found the vertex correctly, but you can't produce -350 items

    • 11 months ago
  8. satellite73 Group Title
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    where on earth did the 280 come from?

    • 11 months ago
  9. mathcalculus Group Title
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    That's the production level that will minimize the average cost

    • 11 months ago
  10. satellite73 Group Title
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    oh, i guess i have no idea what an average cost is

    • 11 months ago
  11. DebbieG Group Title
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    YOu have cost, to find average cost divide that by x. THEN take the derivative, that is marginal average cost. Minimize THAT.

    • 11 months ago
  12. satellite73 Group Title
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    oooooh!

    • 11 months ago
  13. mathcalculus Group Title
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    i did c(X)/x, differentiated, then set it to zero. and got x=280

    • 11 months ago
  14. mathcalculus Group Title
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    how @DebbieG

    • 11 months ago
  15. satellite73 Group Title
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    why is that an "average cost"?

    • 11 months ago
  16. mathcalculus Group Title
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    The minimal average cost?

    • 11 months ago
  17. DebbieG Group Title
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    Because C(x) gives the total cost of producing x items. So C(x)/x gives the average cost per item, at the production level x.

    • 11 months ago
  18. mathcalculus Group Title
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    okaay but let's find part e please.

    • 11 months ago
  19. satellite73 Group Title
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    learn something new every day

    • 11 months ago
  20. DebbieG Group Title
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    Sorry - I didn't mean to minimize the derivative... lol... I meant to minimize the average cost. Which you can do by setting the derivative of it =0. :)

    • 11 months ago
  21. mathcalculus Group Title
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    that's my main concern...

    • 11 months ago
  22. DebbieG Group Title
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    So you have average cost: A(x)=78400/x+700+x Take that derivative, set it = 0, and that's where your average cost is minimized.

    • 11 months ago
  23. mathcalculus Group Title
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    i did

    • 11 months ago
  24. mathcalculus Group Title
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    x=280

    • 11 months ago
  25. mathcalculus Group Title
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    i don't understand

    • 11 months ago
  26. DebbieG Group Title
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    OK, you good for e now?

    • 11 months ago
  27. mathcalculus Group Title
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    yes

    • 11 months ago
  28. DebbieG Group Title
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    Sorry - don't understand what?

    • 11 months ago
  29. mathcalculus Group Title
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    but it's wrong.

    • 11 months ago
  30. mathcalculus Group Title
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    d) The production level that will minimize the average cost = 280. which is correct. e) The minimal average cost= ???

    • 11 months ago
  31. DebbieG Group Title
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    What did you get?

    • 11 months ago
  32. DebbieG Group Title
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    Just evaluate the average cost function at x=280

    • 11 months ago
  33. mathcalculus Group Title
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    so plug x into ?

    • 11 months ago
  34. DebbieG Group Title
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    The average cost function: A(x)=78400/x+700+x which is just C(x)/x

    • 11 months ago
  35. DebbieG Group Title
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    what did you get? :)

    • 11 months ago
  36. mathcalculus Group Title
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    right.280!

    • 11 months ago
  37. mathcalculus Group Title
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    well -78400/x^2+1...

    • 11 months ago
  38. mathcalculus Group Title
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    then set it to zero right? @DebbieG

    • 11 months ago
  39. DebbieG Group Title
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    wha? no.... you found the production level that minimizes average cost already, by setting the derivative of average cost = 0, right? Now you just need to know what that average cost is - what is the average cost at that production level of x=280 So PLUG x=280 INTO the average cost function.

    • 11 months ago
  40. mathcalculus Group Title
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    oooooooo

    • 11 months ago
  41. mathcalculus Group Title
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    how about if i want to find the production level that will maximize profit.

    • 11 months ago
  42. mathcalculus Group Title
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    @DebbieG

    • 11 months ago
  43. DebbieG Group Title
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    Then you need the profit function. Then find where it is maximized, by taking its derivative and set it = 0.

    • 11 months ago
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