## mathcalculus Group Title FIND: The minimal average cost (ATTACHED.) 10 months ago 10 months ago

1. mathcalculus Group Title

2. satellite73 Group Title

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

3. satellite73 Group Title

oh, i see you did that. hmmmm

4. satellite73 Group Title

weird i guess to minimize the cost, produce nothing

5. mathcalculus Group Title

?

6. mathcalculus Group Title

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

7. satellite73 Group Title

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

8. satellite73 Group Title

where on earth did the 280 come from?

9. mathcalculus Group Title

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

10. satellite73 Group Title

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

11. DebbieG Group Title

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

12. satellite73 Group Title

oooooh!

13. mathcalculus Group Title

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

14. mathcalculus Group Title

how @DebbieG

15. satellite73 Group Title

why is that an "average cost"?

16. mathcalculus Group Title

The minimal average cost?

17. DebbieG Group Title

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 Group Title

okaay but let's find part e please.

19. satellite73 Group Title

learn something new every day

20. DebbieG Group Title

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 Group Title

that's my main concern...

22. DebbieG Group Title

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 Group Title

i did

24. mathcalculus Group Title

x=280

25. mathcalculus Group Title

i don't understand

26. DebbieG Group Title

OK, you good for e now?

27. mathcalculus Group Title

yes

28. DebbieG Group Title

Sorry - don't understand what?

29. mathcalculus Group Title

but it's wrong.

30. mathcalculus Group Title

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

31. DebbieG Group Title

What did you get?

32. DebbieG Group Title

Just evaluate the average cost function at x=280

33. mathcalculus Group Title

so plug x into ?

34. DebbieG Group Title

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

35. DebbieG Group Title

what did you get? :)

36. mathcalculus Group Title

right.280!

37. mathcalculus Group Title

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

38. mathcalculus Group Title

then set it to zero right? @DebbieG

39. DebbieG Group Title

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 Group Title

oooooooo

41. mathcalculus Group Title

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

42. mathcalculus Group Title

@DebbieG

43. DebbieG Group Title

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