(a)

The open box has a square base.

Volume = area of the base(height).

In this case area of the base .

Volume of the box cubic feet.

.

Solve for .

.

Find the area of remaining four sides of the box.

Area of the four sides is .

Substitute in .

.

Total area = .

(b)

Substitute in .

square feet material is required.

(c)

Substitute in .

square feet material is required.

(d)

Graph the function .

Graph of the function :

Locate the minimum point on the graph of .

is smallest when ft.

(a) .

(b) square feet.

(c) square feet.

(d)

Graph of the function :

is smallest when ft.