Question

please help me!
A jewelry store is designing a gift box. the sum of the length, width and height is 12 inches. If the length is one inch greater in height, what should the dimensions of the box be to maximize its volume? what is the maximized volume?

Answer 1

V = L W H = (H+1) W H = H^2W + WH
L+W+H = 12 = (H+1) + W + H = W + 2H+1
W=11- 2H

Make V(H) only and set dH/dH = 0 to get extreme's value of H
check that (d/dH) (dV/dH) < 0 so answer is max not min

Answer 2

huh

Answer 3

To maximize a function, want to get it to depend on nly one variable
Here, we start with L, W, H. It seems that L=H+1, so we can make that substitution.
We then have H and W. Putting W in terms of H, we now have volume as a function of H, which you maximize by setting dV(H)/dH = 0. If you do not know this technique, the problem is not suitable for you.

Answer 4

can you show work? i am a visual learner

Answer 5

please @douglaswinslowcooper

Answer 6

@douglaswinslowcooper I think you will have to write them all using the same variable.

Answer 7

im so confused by this im doing a chapter review

Answer 8

Yes, the idea is to boil the relationships down to one variable, such as H..

I must leave.

Answer 9

uuuh ok? & then whatr

Answer 10

I think this guy would be able to help you.

@iPwnBunnies
@hartnn
@FibonacciChick666

Any of these should come here.

Answer 11

so if we can start a new? can you draw me a picture to represent the box?

Answer 12

its just on my worksheet

Answer 13

i mean can you yourself draw a picture

Answer 14

idk how lol id just draw a 3d cube

Answer 15

is a 3d cube a good enough representation for the box?

Answer 16

in your mind?

Answer 17

i guess

Answer 18

so draw it

Answer 19

i did

Answer 20

on here