## brendakayyy 2 years ago help me with optimization for calculus

1. brendakayyy

a computer company determines its profit equation in millions of dollars given by p=x^3-48x^2+720x-1000 where x is the number of thousands of units of software sold

2. brendakayyy

and 0<x<40 optimize the manufactures profit

3. Goten77

im thinking this is really ez.... but maybe im wrong.... since from 0-40 it looks like a line almost.... wouldnt (40,y) b the maximum?

4. Goten77

or maybe im wrong

5. zepdrix

|dw:1355889094401:dw|It's a cubic function, so it's going to have this shape. As I've illustrated in the picture, it is possible that 40 might not be the maximum profit value. So we'll have to do some work to find out where that point is.

6. brendakayyy

do i differentiate the function and find the critical values?

7. zepdrix

$\large P(x)=x^3-48x^2+720x-1000$Yes very good. You'll want to find Critical Points, and since this is a CLOSED INTERVAL, also check the END POINTS! Then simply plug each value into the function, and see which gives you the largest output.

8. Goten77

oh if thats how it looked then i graphed it wrong.. my bad

9. zepdrix

Hmm I better throw it into wolfram and make sure I'm not way off.. cause I was just doing that based off of memory :P

10. Goten77

but anyways it be best to just find derivative.. and critical points.. then find values of those and the 0/40 and then u get ur answer

11. brendakayyy

would my critical values be x<12, 12<x<20, X>20?

12. Goten77

ur critical valued would be points.....

13. Goten77

|dw:1355889480030:dw|

14. zepdrix

You got the correct points, x=12, x=20. I'm not sure why you wrote them as intervals though :)

15. Goten77

^ye

16. zepdrix

Now you want to plug your values into P(x) and compare, to find out which one gives you the largest value within this closed interval.$\large P(12),\quad P(20), \quad P(0), \quad P(40)$

17. brendakayyy

well cuz you base your values off the intervals according to my teacher

18. brendakayyy

what equation would i plug that into?

19. zepdrix

The original equation.

20. brendakayyy

ok got it

21. brendakayyy

whered you get the P(40) and P(0)

22. Goten77

there apart of the domain.. so there possible maxs's mins

23. brendakayyy

oh thats what was meant by end points so if it were aclosed interval i would not take the end points into consideration right?

24. brendakayyy

what are the dimensions of the square based open top box that has a volume of 20 cubic inches and smallest surface area?

25. brendakayyy

can someone help me with this one ^

26. Zarkon

if you have a new question you should put it in a new thread