1. An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize the surface area?

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Direction: Analyze the given problem. Show your complete and detailed solution (Given, Unknown, Solution,
and Answer).
1. An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize
the surface area?
2. You are under contract to design a storage building with a square base and a volume of 14,000 cubic
feet. The cost of materials is $4 per square foot for the floor, $16 per square foot for the walls and $3
per square foot for the roof. Find the dimensions that minimize the cost of materials.
3.
A total of 2,000 square feet is to be enclosed in two pens. The outside walls are to be constructed of
brick and the inner dividing wall is to be constructed of chain link. The brick wall costs $10 per linear
foot and the chain link costs $5 per linear foot. Find the dimensions x and y that minimize the
construction cost.
Transcribed Image Text:Direction: Analyze the given problem. Show your complete and detailed solution (Given, Unknown, Solution, and Answer). 1. An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize the surface area? 2. You are under contract to design a storage building with a square base and a volume of 14,000 cubic feet. The cost of materials is $4 per square foot for the floor, $16 per square foot for the walls and $3 per square foot for the roof. Find the dimensions that minimize the cost of materials. 3. A total of 2,000 square feet is to be enclosed in two pens. The outside walls are to be constructed of brick and the inner dividing wall is to be constructed of chain link. The brick wall costs $10 per linear foot and the chain link costs $5 per linear foot. Find the dimensions x and y that minimize the construction cost.
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