Chocolate Box Company is going to make open-topped boxes out of 9 × 14-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?

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Chocolate Box Company is going to make open-topped boxes out of 9 × 14-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?

Mathematics
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9-2x = width 14-2x = length x = height Area of a box is: WLH A = (9-2x)(14-2x)(x) A = (9-2x)(14x-2x^2) A = 126x -18x^2 - 28x^2 +4x^3 A = 4x^3 -46x^2 +126x get the derivative and solve it for 0: Dx(A) = 12x^2 -92x +126 = 0 This would be easier if I had pencil and paper handy :)
the answer will have to fall between 0 and 9, so we can throw out anything that is out of those bounds.
x^2 - (92/12)x +(92/24)^2 = -(126/12) + (92/24)^2 (x - (92/24))^2 = -(6048/576) + (8464/576) x - 92/24 = +-sqrt(2416)/24 x = +-sqrt(2416)/24 + 92/24 x = 5.881 or x= 1.785 remember that x is doubled; so 5.88 doubled is over 9 I would say that x would be about 1.785 :=: 2 A = (9-2(2)) (14-2(2))(2) A = (5)(10)(2) A = 25 cubic inches if I did it right :)

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And of course I would forget how to multiply after all that ... lol 5(10) = 50; 50(2) = 100 A equals about 100 cubic inches....
101.09329869793039430976432210189 if you want to be more accurate :)
THANK YOU!!! Amistre64 it was right...your a life saver.
amistre64 is correct

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