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