Question

Clemson University Packaging Science Department has asked its freshmen students to construct an open-topped box from a piece of cardboard 30 inches by 70 inches by cutting out squares of width x from the corners and folding up the flaps. What dimensions would produce the greatest volume? What is that volume?Round answers to the nearest tenth.Length = _____ inchesWidth = _____ inchesHeight = _____ inchesMax Volume = _____ inches

Answer 1

Volume = x(70 - 2x)(30 - 2x)

= x(2100 - 200x + 4x^2)

= 2100x - 200x^2 + 4x^3

Volume' = 2100 - 400x + 12x^2

12x^2 - 400x + 2100 = 0

6x^2 - 200x + 1050 = 0

x1 = 6.5 x2 = 26.8

Lenght = 57 in

width = 17 in

height = 6.5

Max volume = 6298.5 in^3