# Math

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An open box is to be made from a 10-ft by 14-ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and folding up the sides. what size squares should be cut to obtain a box with largest possible volume?

• Math -

let each side of the cut-out-squares be x ft
so the box will be 10-2x y 14-2x by x

V = x(10-2x)(14-2x)
= x(140 -48x + 4x^2)
= 140x - 48x^2 + 4x^3
d(V)/dx = 140 - 96x + 12x^2 = 0 for a max of V
3x^2 - 24x + 35 = 0
x = (24 ± √156)/6
= appr. 1.92 or 6.08 , but obviously 10-2x > 0 ---> x > 5

cut out should be 1.92 ft by 1.92 ft

check my arithmetic

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