Question

If 1,200 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.

Answer 1

is this a calculus problem?

Answer 2

yes calc ab.

Answer 3

I got 45,000

Answer 4

what is your equation for volume?

Answer 5

300x - x^3/2

Answer 6

1,200 = b^2 + 4bh

hmm, have you done langrange multipliers?

Answer 7

langrange multipliers? Never heard of them. this is just applied min and max problems

Answer 8

V = b^2h ; A = b^2+4bh-1200 = 0

Vb = 2bh; L~Ab = L(2b+4h)
Vh = b^2; L~Ah = L(4b)

equating partials we have

4Lb = b^2, b=4L

2bh = 2Lb+4Lh

bh-2Lh = Lb

h(b-2L) = Lb

h = Lb/(b-2L) = 2L
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3L^2 = 75

L=5
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b=20, h=10 is what im getting ... if i did a proper langrange :)

Answer 9

i tried doing a min max setup but i wasnt getting anywhere useful, so i attempted the langrange

Answer 10

Okay that's long-range that's what we do as well. so because b=20 and h=10 the volume then we get lwh=20(10)(5)=1000?

Answer 11

we could take our volume in terms of b given that

b^2+4bh-1200 = 0

h = (1200-b^2)(4b)^(-1)

V = b^2(1200-b^2)(4b)^(-1)

or

V = (1200b -b^3)/4

Answer 12

no, 20*20*10

Answer 13

Did you get the second 20 from b^2+4bh-1200 = 0

Answer 14

V = (1200b -b^3)/4

V' = (1200-3b^2)/4 = 0

1200-3b^2 = 0

1200 = 3b^2

400 = b^2 ; b=20

Answer 15

ohh ok i forgot to take the derivative of v.

Answer 16

no, i got b (the base) from the workings ... the base has a side length of 20

Answer 17

Okay, I understand now, thank you for helping me!

Answer 18

youre welcome