Rectangular container optimization

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To optimize the cost of a rectangular storage container with a volume of 10 m^3 and a base length twice its width, the cost of materials must be calculated based on the base and sides. The base costs $10 per square meter, while the sides cost $6 per square meter. A participant is struggling with their calculations, resulting in incorrect negative values. They are advised that their expression for height in relation to width may be incorrect. Accurate formulation of dimensions is crucial for determining the minimum material cost effectively.
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Homework Statement


A rectangular storage container with an open top is to have a volume of 10 m^3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.


Homework Equations



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The Attempt at a Solution


I have my worked out (but wrong) solution here: http://img510.imageshack.us/img510/7963/calchw.jpg
For some reason I keep getting a negative answer. I really have no idea what I'm doing wrong.
 
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Your expression for y in terms of x isn't correct.
 

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