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Emily is making a closed rectangular box with a square base from two different woods. The wood for the top and bottom costs $16 per square metre, and the wood for the sides costs $8 per square metre. If the square base must have a side length between 0.25m and 1m, what are the dimensions of the box that will minimize the cost of wood for a volume of 0.25 cubic metres?

Emily is making a closed rectangular box with a square base from two different woods. The wood for the top and bottom costs $16 per square metre, and the wood for the sides costs $8 per square metre. If the square base must have a side length between 0.25m and 1m, what are the dimensions of the box that will minimize the cost of wood for a volume of 0.25 cubic metres?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Emily is making a closed rectangular box with a square base from two different woods. The wood for the top and bottom costs $16 per square metre, and the wood for the sides costs $8 per square metre. If the square base must have a side length between 0.25m and 1m, what are the dimensions of the box that will minimize the cost of wood for a volume of 0.25 cubic metres?
Transcribed Image Text:3. Emily is making a closed rectangular box with a square base from two different woods. The wood for the top and bottom costs $16 per square metre, and the wood for the sides costs $8 per square metre. If the square base must have a side length between 0.25m and 1m, what are the dimensions of the box that will minimize the cost of wood for a volume of 0.25 cubic metres?
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