## toxicsugar22 5 years ago A computer store sells approximately 300 of its most popular model per year. The manager would like to minimize her annual inventory cost by ordering the optimal numbers of computers, x, at regular intervals. If she orders x computers in each shipment, the cost of storage willl be 6x dollers, and the cost of reording will be 300/x (15x+10) dollers. The inventory cost is the sum of the storage cost and the reording cost. use the distributive law to simplfy the expression for the rerding cost. Then express the inventory cost C as a function of x

1. toxicsugar22

hi dumbcow

2. anonymous

hi

3. toxicsugar22

do any of u guys underand this question

4. anonymous

working on it give me a minute

5. anonymous

is x(x+15) all on denominator or just the x ?

6. anonymous

the simplified version of ur question is 30x^3 + 20x^2 = 300 correct me if am wrong

7. anonymous

is the cost of reording: ???

8. anonymous

${ 300 \over x} (15x+10)$

9. toxicsugar22

yes math mind got it rightd

10. anonymous

isn't it equal to 6? [300/x(15x + 10) = 6\]

11. anonymous

6x that is

12. anonymous

$C = \frac{6(x ^{2}+50x+750)}{x}$

13. anonymous

Then express the inventory cost C as a function of x:$C(x) = 6x+{300 \over x}(15x+10) = 6x+{3000 \over x} + 45000$ is that right?

14. anonymous

oh

15. anonymous

wow i misread the question, i am wrong sorry time for me to leave...haha

16. anonymous

haha. it happens .

17. toxicsugar22

yes math mind got it right

18. toxicsugar22

so it says complete this of valuses for the inventory cost for various reorder size so if x is 10 what isC how would i set that up can u show me

19. anonymous

all yu do i plug 10 for x: $C(10)=6(10)+{3000 \over 10}+45000 = ?$

20. anonymous

$C=\frac{6(x^2+750x+500)}{x}$

21. toxicsugar22

ok i got it

22. toxicsugar22

thanks

23. toxicsugar22

How many computers should the manager order in each shipment so as to minimize the inventury cost

24. anonymous

optimal number of computers to minimize cost is 10sqrt(5)

25. anonymous

took derivative of C and set equal to zero and solve for x

26. anonymous

what formula are yu using cow?

27. toxicsugar22

math mind what do u think

28. anonymous

use the quotient rule since it's a fraction

29. toxicsugar22

How many computers should the manager order in each shipment so as to minimize the inventury cost

30. toxicsugar22

well does anyone know

31. anonymous

sorry.. tv distracted me haha.. i got the same thing as cow 10sqrt{5}

32. anonymous

which is 22.36 computers

33. toxicsugar22

ok thanks and how many orders will she make during the year?

34. toxicsugar22

does anyone know this

35. anonymous

if the stores sell aprox. 300 a year and it orders 22.36 a shipment: 300/22.36 = 13.41 i think that's the answer

36. toxicsugar22

ok thanks

37. toxicsugar22

graph this equation and estimate the possible values for can u do that I graphed it and tried various nubers but it is not ight

38. toxicsugar22

can u try

39. toxicsugar22

like if u have a graphing calculator

40. anonymous

oh sorry, that i can't do :/

41. toxicsugar22

ok

42. toxicsugar22

its okay

43. toxicsugar22

do u know a website tgraph it for me

44. toxicsugar22

do u know any website that will graph it for me

45. toxicsugar22

ok thanks