Math - Business Calc.

Chocolate Box Company is going to make open-topped boxes out of 5 × 17-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way? (Round your answer to the nearest tenth.)

Thank You for the help, I really appreciate it!

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asked by Jerry
  1. L = 17 - 2 h
    W = 5 - 2 h

    V = L W h
    V = (17-2h)(5-2h)h = (17-h)(5h-2h^2)

    dV/dh = (17-h)(5 - 4h) +(5h-2h^2)(-1)

    = 85 - 73 h +4 h^2 -5h + 2 h^2

    = 85 - 78 h + 6 h^2
    where is that derivative zero?
    h = [ 78 +/- sqrt (6084-2040) ]/12

    h = [ 78 +/- 63.6 ] / 12

    h = 11.7 impossible, plank not wide enough
    or
    h = 1.2 inches

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    posted by Damon
  2. Damon, thank you! But i tried entering it in but it said it was wrong.

    Also it wants the answer in inches cubed (in^3)

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    posted by Jerry
  3. Hey, use that h, calculate L and w
    find L W h

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    posted by Damon
  4. Ahhh okay my bad. Thank you!!!

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    posted by Jerry
  5. I noticed an error in Damon's solution

    4th line : V = (17-2h)(5-2h)h = (17-h)(5h-2h^2)
    should be : V = (17-2h)(5-2h)h = (17-2h)(5h-2h^2)

    I had h = 1.1445

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    posted by Reiny

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