44ecbe…: “Around the important tree”

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Worked Out Examples Problem Videos

The following video may be helpful when trying to solve this example. Note that you may skip to the end of the video to get completion credit for this page if you don’t need to watch it.

Practice Problems: Optimization

1 : We want to construct a box whose base length is $\sage {p1boxmulti}$ times the base width. The material used to build the top and bottom cost $ $\sage {p1costtop}$ per square feet and the material used to build the sides cost $ $\sage {p1costedge}$ per square feet. If the box must have a volume of $\sage {p1vol}$ cubic feet determine the dimensions that will minimize the cost to build the box.

Width: $\answer {\sage {p1Width}}$ feet
Length: $\answer {\sage {p1Length}}$ feet
Height: $\answer {\sage {p1Height}}$ feet

When in doubt, draw a picture! Note that the Length should be the dimension that is $\sage {p1boxmulti}$ times larger than the width dimension. Remember it is typically the case that the constraint equation (the set volume here) is used to remove a variable in the extrema equation (the cost equation in this case).