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

1. mathcalculus

2. satellite73

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

3. satellite73

oh, i see you did that. hmmmm

4. satellite73

weird i guess to minimize the cost, produce nothing

5. mathcalculus

?

6. mathcalculus

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

7. satellite73

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

8. satellite73

where on earth did the 280 come from?

9. mathcalculus

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

10. satellite73

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. satellite73

oooooh!

13. mathcalculus

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

14. mathcalculus

how @DebbieG

15. satellite73

why is that an "average cost"?

16. mathcalculus

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. mathcalculus

okaay but let's find part e please.

19. satellite73

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. mathcalculus

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. mathcalculus

i did

24. mathcalculus

x=280

25. mathcalculus

i don't understand

26. DebbieG

OK, you good for e now?

27. mathcalculus

yes

28. DebbieG

Sorry - don't understand what?

29. mathcalculus

but it's wrong.

30. mathcalculus

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. mathcalculus

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. mathcalculus

right.280!

37. mathcalculus

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

38. mathcalculus

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. mathcalculus

oooooooo

41. mathcalculus

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

42. mathcalculus

@DebbieG

43. DebbieG

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