Question

Another optimization problem. This one I really dont know how to do it :)

Answer 1

so I believe is equation is 10 (2x^2) + 2 (4xh)
what to do with the h?

Answer 2

the correct expression should be \[10(x^2)+2(4xh)+2(2x^2)\] since the box is made of tin and velvet on its bottom

Answer 3

isnt only the bottom is lined with velvet?

Answer 4

the expression represents the cost in making the box with velvet at the bottom, so this should be equated to the total cost given in the problem

Answer 5

oh..or is it saying the box is first layered with tin, but the bottom has addition llayer of velvet?

Answer 6

tin layered with velvet

Answer 7

velvet on tin on the bottom, that's what i mean.

Answer 8

ohh ok, yea, thats what i think.
but that's what i did .. what do I do with the h?

Answer 9

uhm, solve h, substitute in the formula for the volume of the box, then maximize the volume of the box.

Answer 10

oh ok, i will try it first, thanks

Answer 11

don't forget to convert $ to cents, since you are using cents in your equation for h.

Answer 12

thks :/ i just realized i had the wrong units after i finished it lol

Answer 13

is it a typo error that velvet costs 10 cents/cm^3?

Answer 14

I think this question has more errors than just that typo

Answer 15

If you follow what it says, then @sirm3d has formulated the correct equation. However, solving that equation leads to a velvet cost of $0.57 which is not in any of the options.
However, if you assume the box does NOT have a top, then we get a solution of $0.67 - which IS one of the options.

Answer 16

Unless I have made an error in my calculations?

Answer 17

what did u get for ur x value?

Answer 18

for a closed box I got: \(x=\sqrt{\frac{120}{21}}\)
for an open box I got: \(x=\sqrt{\frac{20}{3}}\)

Answer 19

ok, then i believe the question suppose to be an open box.. it is 100% possible that they practice problems have mistakes :) thanks

Answer 20

mine are the same as @asnaseer

Answer 21

can u show me how u did it..i'm 0.30 off...

Answer 22

is h = 240 - 12x^2 / 8x

Answer 23

yw :)
the main thing here is that you understand how to solve these types of questions. Matching the right answer is least thing you should worry about. :)

for closed box, I got: \(h=\frac{120-7x^2}{4x}\)
for open box: \(h=\frac{120-6x^2}{4x}\)

Answer 24

It might be better for you to show us your steps so that we can spot where you may have made a mistake.

Answer 25

ohh ok i get it.. i spotted mine rightaway :) it's just i'm not totally 100% understand why sirm had that equation

Answer 26

now i do thanks both of u

Answer 27

keep forgetting the bottom has both velvet and tin

Answer 28

the bottom of the box has sides of length x. so it area is x^2
the vertical sides of the box (4 of them) each have an area of xh

Answer 29

i corrected your expression which represents the cost of the box. from you expression, i conclude that x is the side of the square and h is the height

Answer 30

so, assuming an open box, total surface area for tin would be: x^2 + 4xh
and total surface area for velvet would be: x^2

Answer 31

so the total cost would be:\[2(x^2+4xh)+10x^2=240\]where I have converted everything to cents

Answer 32

yea, now i really do get it :) i will just do both open box and closed box for more practice then!

Answer 33

good idea - its great to see someone who is eager to learn! :)