Determine function with volume

Question

Using a 10-in. by 12-in. piece of cardboard, you construct a box with a lid. Write a function giving the volume of the box in terms of x

Answer 1

x y x y

+--+----+--+----+

| | | | | x

+--+----+--+---+

| | | | |

| | | | | z

+--+---+--+----+

| | | | | x

+--+---+--+----+

2x +2y = 10

2x +z = 12 --> z = 12 - 2x

x+y = 5 --> y = 5-x

Volume, V = xyz = x(5-x)(12-2x) = 2x³-22x²+60x

If you let x = 1 inch, y = 4 , z = 10, V = 40 in³