3. Kip and Garrett are designing a rectangular storage container with an open top. They decide it will have a volume of 10 m³, and the length of its base will be twice the width. They'd like to be environmentally friendly, so they'd like to make the container's surface area as small as possible.
model the container's surface area as a function of a The first step in this optimization problem is single variable. That's what you'll do in this problem.
(a) Express the container's surface area as a function of its width.
(b) Express the container's surface area as a function of its height.
Start with three variables: l for length, w for width, and h for height.
Express the thing you're trying to model (the container's surface area) in terms of l, w, and h.
• Now, look for relationships among l, w, and h. (If you're having trouble with this, try thinking about some concrete scenarios. Could the box have length 1 m, width 1 m, and height 1 m? Why or why not? Could the box have length 2 m, width 1 m, and height 1 m? Why or why not?)
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