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tmagloire1

  • one year ago

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.

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  1. amistre64
    • one year ago
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    is this a calculus problem?

  2. tmagloire1
    • one year ago
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    yes calc ab.

  3. tmagloire1
    • one year ago
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    I got 45,000

  4. amistre64
    • one year ago
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    what is your equation for volume?

  5. tmagloire1
    • one year ago
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    300x - x^3/2

  6. amistre64
    • one year ago
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    1,200 = b^2 + 4bh hmm, have you done langrange multipliers?

  7. tmagloire1
    • one year ago
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    langrange multipliers? Never heard of them. this is just applied min and max problems

  8. amistre64
    • one year ago
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    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 ---------------- 3L^2 = 75 L=5 -------------- b=20, h=10 is what im getting ... if i did a proper langrange :)

  9. amistre64
    • one year ago
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    i tried doing a min max setup but i wasnt getting anywhere useful, so i attempted the langrange

  10. tmagloire1
    • one year ago
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    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?

  11. amistre64
    • one year ago
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    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

  12. amistre64
    • one year ago
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    no, 20*20*10

  13. tmagloire1
    • one year ago
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    Did you get the second 20 from b^2+4bh-1200 = 0

  14. amistre64
    • one year ago
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    V = (1200b -b^3)/4 V' = (1200-3b^2)/4 = 0 1200-3b^2 = 0 1200 = 3b^2 400 = b^2 ; b=20

  15. tmagloire1
    • one year ago
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    ohh ok i forgot to take the derivative of v.

  16. amistre64
    • one year ago
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    no, i got b (the base) from the workings ... the base has a side length of 20

  17. tmagloire1
    • one year ago
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    Okay, I understand now, thank you for helping me!

  18. amistre64
    • one year ago
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    youre welcome

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