## anonymous 2 years ago FIND: The minimal average cost (ATTACHED.)

1. anonymous

2. anonymous

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

3. anonymous

oh, i see you did that. hmmmm

4. anonymous

weird i guess to minimize the cost, produce nothing

5. anonymous

?

6. anonymous

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

7. anonymous

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

8. anonymous

where on earth did the 280 come from?

9. anonymous

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

10. anonymous

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

11. DebbieG

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

12. anonymous

oooooh!

13. anonymous

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

14. anonymous

how @DebbieG

15. anonymous

why is that an "average cost"?

16. anonymous

The minimal average cost?

17. 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.

18. anonymous

okaay but let's find part e please.

19. anonymous

learn something new every day

20. 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. :)

21. anonymous

that's my main concern...

22. 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.

23. anonymous

i did

24. anonymous

x=280

25. anonymous

i don't understand

26. DebbieG

OK, you good for e now?

27. anonymous

yes

28. DebbieG

Sorry - don't understand what?

29. anonymous

but it's wrong.

30. anonymous

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

31. DebbieG

What did you get?

32. DebbieG

Just evaluate the average cost function at x=280

33. anonymous

so plug x into ?

34. DebbieG

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

35. DebbieG

what did you get? :)

36. anonymous

right.280!

37. anonymous

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

38. anonymous

then set it to zero right? @DebbieG

39. 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.

40. anonymous

oooooooo

41. anonymous

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

42. anonymous

@DebbieG

43. DebbieG

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