a sheet of cardboard is to be folded up to make a closed box. If the cardboard measures 55 cm by 80cm calculate the maximum volume of the box that can be made from this sheet of cardboard

Answer 1

let each side of the squares to be cut out be x cm
length = 80-2x
width = 55-2x , 0 < x < 27.5
height = x

V = x(80-2x)(55-2x)
= 4x^3 -270x^2 + 4400x

dV/dx = 12x^2 - 540x + 4400
= 0 for a max of V

3x^2 - 135x + 1100 = 0
x = (135 ± √5025)/6

take it from there (I get x = appr 10.69)