A box with an open top is to be constructed by cutting equal-sized squares out of the corners of a 18 inch by 30 inch piece of cardboard and folding up the sides.

Question

a) Let w be the length of the sides of the cut out squares. Determine a function V that describes the volume of the finished box in terms of w.
V(w) =

b) What width w would maximize the volume of the box?
w = inches

c) What is the maximum volume?
V = cubic inches

Answer 1

V(w) = (18-2w)(30-2w)

max V where dV/dw = 0

Answer 2

Oops. base * height is volume

V(w) = (18-2w)(30-2w)w

Answer 3

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