Rectangular container optimization

In summary, the conversation discusses finding the cost of materials for the cheapest rectangular storage container with a volume of 10 m^3. The base of the container has a length that is twice the width, and materials for the base cost $10 per square meter while materials for the sides cost $6 per square meter. The individual has a worked out solution but is getting a negative answer and is unsure of where they went wrong. Their expression for y in terms of x is incorrect.
  • #1
hks118
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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.
 
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  • #2
Your expression for y in terms of x isn't correct.
 

1. How can I determine the optimal size of a rectangular container?

The optimal size of a rectangular container can be determined by considering the dimensions of the objects that need to be stored or transported in the container, as well as any constraints such as weight or volume limitations. Mathematical optimization techniques can also be used to find the most efficient size.

2. What factors should be considered when optimizing a rectangular container?

Factors that should be considered when optimizing a rectangular container include the dimensions of the objects, the weight and volume limitations, the shape and strength of the container, and the method of transportation or storage.

3. How can I minimize wasted space in a rectangular container?

To minimize wasted space in a rectangular container, it is important to consider the shapes and sizes of the objects being stored or transported and arrange them in a way that fills the container as efficiently as possible. The use of dividers or stacking techniques can also help to maximize space utilization.

4. What are some common problems that can arise in rectangular container optimization?

Some common problems that can arise in rectangular container optimization include overpacking (where objects are crammed into the container, potentially causing damage), underpacking (where there is unused space in the container), and container instability (where the objects are not arranged in a way that ensures the stability of the container during transportation).

5. How can I improve the efficiency of a rectangular container?

The efficiency of a rectangular container can be improved by using mathematical optimization techniques, considering the shapes and sizes of the objects being stored or transported, and utilizing dividers or stacking techniques. Regular review and optimization of the container's contents can also help to continuously improve its efficiency.

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