Question

FIND: The minimal average cost (ATTACHED.)

Answer 1

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

Answer 2

oh, i see you did that.
hmmmm

Answer 3

weird
i guess to minimize the cost, produce nothing

Answer 4

?

Answer 5

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

Answer 6

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

Answer 7

where on earth did the 280 come from?

Answer 8

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

Answer 9

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

Answer 10

YOu have cost, to find average cost divide that by x.

THEN take the derivative, that is marginal average cost.

Minimize THAT.

Answer 11

oooooh!

Answer 12

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

Answer 13

how @DebbieG

Answer 14

why is that an "average cost"?

Answer 15

The minimal average cost?

Answer 16

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.

Answer 17

okaay but let's find part e please.

Answer 18

learn something new every day

Answer 19

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. :)

Answer 20

that's my main concern...

Answer 21

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.

Answer 22

i did

Answer 23

x=280

Answer 24

i don't understand

Answer 25

OK, you good for e now?

Answer 26

yes

Answer 27

Sorry - don't understand what?

Answer 28

but it's wrong.

Answer 29

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

e) The minimal average cost= ???

Answer 30

What did you get?

Answer 31

Just evaluate the average cost function at x=280

Answer 32

so plug x into ?

Answer 33

The average cost function:

A(x)=78400/x+700+x

which is just C(x)/x

Answer 34

what did you get? :)

Answer 35

right.280!

Answer 36

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

Answer 37

then set it to zero right? @DebbieG

Answer 38

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.

Answer 39

oooooooo

Answer 40

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

Answer 41

@DebbieG

Answer 42

Then you need the profit function. Then find where it is maximized, by taking its derivative and set it = 0.