You want to build a rectangular box to hold 1m³ of material. The length of the base of the box must be twice the width of the base of the box. What is the least amount of material you can use to build the box.

2a) Write equation for the quantity you are optimizing. This equation will be in terms of x and h and should be fully simplified.

2b) Write equation for the given information.

2c) Use the given information to write the equation in 2a in terms of a single variable x. Simplify this equation so it is in the form of a rational equation.

2d) Use technology to graph your equation and find the value of x that minimizes your equation. Round this value to two decimal places.

2e) State the length and width and height of the box with all values rounded to two decimal places.

2f) Calculate the volume of your box. Does it equal 1? It should be close to one but there will be round off error.