FIND: The minimal average cost (ATTACHED.)

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FIND: The minimal average cost (ATTACHED.)

Mathematics
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minimum is at the vertex compute \(-\frac{b}{2a}\) with \(b=700,a=1\)
oh, i see you did that. hmmmm

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

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