Question

Help?


A rectangular storage container with an open top is to have a volume of 18 cubic meters. The length of its base is twice the width. Material for the base costs 13 dollars per square meter. Material for the sides costs 7 dollars per square meter. Find the cost of materials for the cheapest such container.

Answer 1

I alread have w^3=378/52
which is 7.27

What should I do step by step next????

Answer 2

i think it's

w^3=252/54 to match your answer?

Answer 3

hw did u get w^3 = 378/52 ?

Answer 4

could be wrong though

Answer 5

i'm rushing it's due in like 33 mins hehe

Answer 6

im aslo getting w^3 = 378/54,

Answer 7

when u let f'(w) = 0

Answer 8

yes that's right i just recheck it

Answer 9

so what do i need to do next?

Answer 10

find value 'w', and substitute in cost function ?

Answer 11

w = cuberoot(378/52)

Answer 12

yeah= 8.088453308456256

Answer 13

whats 8.088 ?

Answer 14

wolfram says cost is ~ 293

http://www.wolframalpha.com/input/?i=26*%281.937%29%5E2+%2B+378%2F%281.937%29

Answer 15

\[\text{The volume of a rectangular prism is as follows.}\\
\ \ \ V = lwh\\
\text{Given as follows.}\\
\ \ \ V = 18\\
\ \ \ l = 2w\\
\text{Derive for the area of the base and sides, respectively.}\\
\ \ \ A_1 = lw\\
\ \ \ A_2 = 2h(w + l)\\
\text{Let's try to reduce our volume equation.}\\
\ \ \ 18 = 2w^2h\\
\ \ \ h = 9w^{-2}\\
\text{Derive the cost function.}\\
\ \ \ C(w) = 13A1 + 7A2\\
\ \ \ \ \ \ \ \ \ \ \ = 13lw + 14h(w+l)\\
\ \ \ \ \ \ \ \ \ \ \ = 26w^2 + 42hw\\
\ \ \ \ \ \ \ \ \ \ \ = 26w^2 + 378w^{-1}\\
\text{Now, let's differentiate it for optimization.}\\
\ \ \ C'(w) = 52w - 378w^{-2}\\
\text{Let's determine the optimal width, }w^*.\\
\ \ \ C'(w*) = 52w^* - 378w^{*-2}\\
\ \ \ 0 = 52w^* - 378w^{*-2}\\
\ \ \ 378w^{*-2} = 52w^*\\
\ \ \ 378 = 52w^{*3}\\
\ \ \ w*^3 = \frac{378}{52}\\
\ \ \ w* = [\frac{378}{52}]^{\frac13}\\
\text{Now we know the optimal width, so let's calculate it's cost.}\\
\\C(w*) = 26[\frac{378}{52}]^\frac23 + 378[\frac{378}{52}]^{-\frac{1}3}\\
\ \ \ \ \ \ \ \ \ \ \simeq292.70
\]

Answer 16

thanks guys!!!

Answer 17

Who wants a medal? And who want me to be his fan?

Answer 18

lol you're my fan already n u gave me many medals before... :)

Answer 19

I think whoever wants to manually simplify the cost at the end deserves as many medals as possible... :-)

Answer 20

Oh K OB thanks ganeshie8! I'm ur fan in heart! :)

Answer 21

that word keeps me motivated me for next problem ;)