Question: A rectangular storage container with an open top is to have a volume of 8 m^3. The length of the base is twice the width.

A rectangular storage container with an open top is to have a volume of 8 m^3. The length of the base is twice the width. Material for the base costs $1.50 per square meter and material for the sides costs $2 per square meter. Find the cost of the material for the cheapest such container. (show work for all)

a) Draw and label a sketch, identifying constants and variables.

b) Create equations relevant to the context of the problem, using the information given. One of these should describe the quantity to be optimized.

c) Find the minimum cost of the material for the container.

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