a 5cm by 5cm square is cut from each corner of a rectangular piece of cardboard.the sides are folded up to make an open box with a maximum volume.if the perimeter of the base is 50cm,what are the dimensions of the box.

3 answers

let the width of the base be x
let the length of the base by y
2x + 2y = 50
x + y = 25 ---> y = 25-x

volume = V = 5xy
= 5x(25-x)
= 125x - 5x^2
dV/dx = 125 - 10x = 0 for a max of V
10x = 125
x = 12.5
y = 12.5

the box is 12.5 by 12.5 by 5 cm

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