Question

Okay, I have a test in 8 Hours and I don't know how to do this. Can someone explain the steps for me to memorize.

1. A company wishes to manufacture a box with a volume of 36 ft3 that is open on top and is twice as long as it is wide.

(a) Let x be the length of the box (so the width is 2x), and let y be the height of the box.
First write the surface area of the box as a function of x and y. Then use the fact that
the volume is 36 cubic feet to write the surface area as a function of x only.

(b) Find the dimensions of the box that will lead to the minimum surface area.

(c) What is the minimum surface area?

Answer 1

Here is the solultion:

a.) Surface Area = 2x^2 + 6xy = 2x^2 = 108/x
b.) x=3 y=2
c.) 30 square feet.

I need to learn the steps to solve these

Answer 2

my book has it laid out in a bunch of sections and its gonna take too long to cipher through it all.

Answer 3

vol=36=(2*x)*x*y=>y=18/(x*x)
surface area=(2*x)*x+2*y*x+2*y*(2*x)=2*x*x+6*x*y
now put y in this......then differentiate w.r.t x and equate it to zero for maximization...to get x=3*cuberoot(2)....once u know x,u know everything.....

Answer 4

sorry minimization...

Answer 5

sorry to get x=3

Answer 6

oh sorry this is calc, cant do anything

Answer 7

sorry

Answer 8

:(

Answer 9

did u finish with part a ?

Answer 10

@MercerC

Answer 11

What does he mean by differentiate w.r.t. x?

Answer 12

it just means taking derivative

Answer 13

Followed it up until that part

Answer 14

ok. so from part a, you have the surface area function in x & y
SA = 2x^2 + 6xy ---------------------------(1)

surface area in x :
SA = 2x^2 + 108/x -------------------------(2)

Answer 15

you want to minimize (2), right ?

Answer 16

yes,taking derivative....and you get 4*x-108/(x*x)...when u equate this to 0,u get x=3.

Answer 17

now is there any part u did not get?

Answer 18

Sorry, I'm not as quick. I'm at Put y into this....which I'm guessing you mean the surface area equation which is for x

Answer 19

2*x*x + 6 * (18/x*x) * x ?

Answer 20

yes,this gives 2x*x+108/x as u expected(given in ans)

Answer 21

so I'm on a financial calculator who do I get the cube root of something. the 108/x is throwing me off

Answer 22

how*

Answer 23

18/x^2....what do I need to plug in or how do I need to get rid of the x^2 here?

Answer 24

are u struck?if yes,where?

Answer 25

I don't understand the 108/x

Answer 26

I get that its easy math for you guys, but I'm plugging stuff in on this calculator and jsut can't actually come up with it, which means I'm not gonna get it on the test.

Answer 27

Then I know how to diffrentiate for fxx(x,y) and fyy(x,y) to get 3 and 2 if those are the steps

Answer 28

I'm stupid....6*18 = 108

Answer 29

A Mathematica part solution with comments is attached.

Answer 30

hartnn, so when I differentiate. I use 2x^2 + 6xy?

Answer 31

for x that is

Answer 32

for part b

Answer 33

....getiing it i think

Answer 34

nope i'm not. please help with part b

Answer 35

Finally followed your steps. thanks. It took me a few times to find what I needed, but I got it.

Answer 36

finally!!