anonymous
  • anonymous
FIND: The minimal average cost (ATTACHED.)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
minimum is at the vertex compute \(-\frac{b}{2a}\) with \(b=700,a=1\)
anonymous
  • anonymous
oh, i see you did that. hmmmm

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anonymous
  • anonymous
weird i guess to minimize the cost, produce nothing
anonymous
  • anonymous
?
anonymous
  • anonymous
i understood part d.... it's 280
anonymous
  • anonymous
you found the vertex correctly, but you can't produce -350 items
anonymous
  • anonymous
where on earth did the 280 come from?
anonymous
  • anonymous
That's the production level that will minimize the average cost
anonymous
  • anonymous
oh, i guess i have no idea what an average cost is
DebbieG
  • DebbieG
YOu have cost, to find average cost divide that by x. THEN take the derivative, that is marginal average cost. Minimize THAT.
anonymous
  • anonymous
oooooh!
anonymous
  • anonymous
i did c(X)/x, differentiated, then set it to zero. and got x=280
anonymous
  • anonymous
how @DebbieG
anonymous
  • anonymous
why is that an "average cost"?
anonymous
  • anonymous
The minimal average cost?
DebbieG
  • DebbieG
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.
anonymous
  • anonymous
okaay but let's find part e please.
anonymous
  • anonymous
learn something new every day
DebbieG
  • DebbieG
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. :)
anonymous
  • anonymous
that's my main concern...
DebbieG
  • DebbieG
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.
anonymous
  • anonymous
i did
anonymous
  • anonymous
x=280
anonymous
  • anonymous
i don't understand
DebbieG
  • DebbieG
OK, you good for e now?
anonymous
  • anonymous
yes
DebbieG
  • DebbieG
Sorry - don't understand what?
anonymous
  • anonymous
but it's wrong.
anonymous
  • anonymous
d) The production level that will minimize the average cost = 280. which is correct. e) The minimal average cost= ???
DebbieG
  • DebbieG
What did you get?
DebbieG
  • DebbieG
Just evaluate the average cost function at x=280
anonymous
  • anonymous
so plug x into ?
DebbieG
  • DebbieG
The average cost function: A(x)=78400/x+700+x which is just C(x)/x
DebbieG
  • DebbieG
what did you get? :)
anonymous
  • anonymous
right.280!
anonymous
  • anonymous
well -78400/x^2+1...
anonymous
  • anonymous
then set it to zero right? @DebbieG
DebbieG
  • DebbieG
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.
anonymous
  • anonymous
oooooooo
anonymous
  • anonymous
how about if i want to find the production level that will maximize profit.
anonymous
  • anonymous
@DebbieG
DebbieG
  • DebbieG
Then you need the profit function. Then find where it is maximized, by taking its derivative and set it = 0.

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