Rectangular container optimization

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SUMMARY

The discussion focuses on optimizing the cost of materials for a rectangular storage container with an open top, designed to hold a volume of 10 m³. The base length is specified as twice the width, leading to a cost analysis where the base material is priced at $10 per square meter and the side material at $6 per square meter. Participants identified errors in the formulation of the dimensions and cost calculations, emphasizing the need for accurate expressions to determine the optimal dimensions that minimize costs.

PREREQUISITES
  • Understanding of volume calculations for rectangular prisms
  • Familiarity with cost optimization problems in calculus
  • Knowledge of basic algebra for solving equations
  • Ability to interpret and analyze graphical representations of functions
NEXT STEPS
  • Study optimization techniques in calculus, specifically for geometric shapes
  • Learn how to derive cost functions based on dimensions and material prices
  • Explore methods for solving equations involving multiple variables
  • Investigate graphical methods for visualizing cost versus dimensions
USEFUL FOR

Students in mathematics or engineering fields, particularly those focusing on optimization problems, as well as professionals involved in cost analysis and material management for construction projects.

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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



See below

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.
 
Last edited by a moderator:
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Your expression for y in terms of x isn't correct.
 

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