FIND: The minimal average cost (ATTACHED.)

- anonymous

FIND: The minimal average cost (ATTACHED.)

- schrodinger

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- anonymous

##### 1 Attachment

- anonymous

minimum is at the vertex
compute \(-\frac{b}{2a}\) with \(b=700,a=1\)

- anonymous

oh, i see you did that.
hmmmm

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## More answers

- anonymous

weird
i guess to minimize the cost, produce nothing

- anonymous

?

- anonymous

i understood part d.... it's 280

- anonymous

you found the vertex correctly, but you can't produce -350 items

- anonymous

where on earth did the 280 come from?

- anonymous

That's the production level that will minimize the average cost

- anonymous

oh, i guess i have no idea what an average cost is

- DebbieG

YOu have cost, to find average cost divide that by x.
THEN take the derivative, that is marginal average cost.
Minimize THAT.

- anonymous

oooooh!

- anonymous

i did c(X)/x, differentiated, then set it to zero. and got x=280

- anonymous

how @DebbieG

- anonymous

why is that an "average cost"?

- anonymous

The minimal average cost?

- 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

okaay but let's find part e please.

- anonymous

learn something new every day

- 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

that's my main concern...

- 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

i did

- anonymous

x=280

- anonymous

i don't understand

- DebbieG

OK, you good for e now?

- anonymous

yes

- DebbieG

Sorry - don't understand what?

- anonymous

but it's wrong.

- anonymous

d) The production level that will minimize the average cost = 280. which is correct.
e) The minimal average cost= ???

- DebbieG

What did you get?

- DebbieG

Just evaluate the average cost function at x=280

- anonymous

so plug x into ?

- DebbieG

The average cost function:
A(x)=78400/x+700+x
which is just C(x)/x

- DebbieG

what did you get? :)

- anonymous

right.280!

- anonymous

well -78400/x^2+1...

- anonymous

then set it to zero right? @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

oooooooo

- anonymous

how about if i want to find the production level that will maximize profit.

- anonymous

@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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