posted by Sejul .
have 50 sq ft of material to make an open top box with a square base.
a) use formula for surface area to express the height h of the box in terms of x.
b) find the dimensions of the box that will produce the maximum volume.
side of square = x
height = h
surface area = x^2 + 4xh
x^2 + 4xh = 50
h = (50 - x^2)/4x
v = hx^2 = (50-x^2)/4x * x^2
v = x(50-x^2)/4
v has a max at x = 5sqrt(2/3) = 4.08
so, a box 4 x 4 x 17/8 will have maximum volume of 34