How Can I Optimize Dimensions for Garden Boxes with Minimal Material?

In summary, the speaker is trying to build garden boxes this summer and is looking to determine the dimensions through optimization. They want the volume to be 13.5ft^3 and the height of the frame to be 8 inches, and they want to minimize the amount of material used. However, they are struggling to model the problem mathematically and are more concerned with the method than the answer. They also mention the real-world complexities of using standard lengths of materials.
  • #1
dcheney214
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Im trying to build garden boxes this summer and I am trying to determine the dimensions through optimization. Its been a long time since I've done this and I can't seem to model this mathematically.

Id like a box where the volume=13.5ft^3 and the height of the frame to be 8 inches or .66ft. Id like to minimize the amount of material used.
I guess I am more bothered that this is a fairly simple problem and I can't remember how to model it. I am more concerned with the method than the answer.

Thanks.
 
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  • #2
dcheney214 said:
Id like to minimize the amount of material used.
I guess I am more bothered that this is a fairly simple problem and I can't remember how to model it.

It isn't a simple problem in the real world. For example, materials such as lumber are usually available only in standard lengths. If you need a 5 ft board from 8 ft lumber and don't use the 3 ft "scrap" left over then you must account for what is wasted in your tally of "amount of material".

If you ignore such real world aspects you can begin by writing the expression for the total amount of material in terms of variables representing the (as yet unknown) dimensions of the box. Do that and someone can help you proceed. (For example, we don't know if your box has a bottom or whether it is just a "frame".)
 

FAQ: How Can I Optimize Dimensions for Garden Boxes with Minimal Material?

1. How do I choose the best location for my garden boxes?

The best location for your garden boxes would be in an area that receives at least 6-8 hours of sunlight per day and has good drainage. It is also important to consider the proximity to a water source and the accessibility for maintenance.

2. What materials should I use to build my garden boxes?

The most commonly used materials for garden boxes are untreated cedar, redwood, or cypress wood. These types of wood are naturally resistant to decay and can last for several years. You can also use composite materials or repurposed materials such as old pallets, but make sure they are safe for growing food.

3. How deep should my garden boxes be?

The ideal depth for garden boxes is between 6-12 inches. This will provide enough room for the roots of most plants to grow, while also allowing for good drainage and aeration of the soil.

4. Do I need to add anything to the soil in my garden boxes?

It is recommended to add a layer of organic compost or fertilizer to the soil in your garden boxes before planting. This will provide essential nutrients for your plants to grow and thrive.

5. How often should I water my garden boxes?

The frequency of watering your garden boxes will depend on the type of plants you are growing and the weather conditions. Generally, it is recommended to water deeply at least 2-3 times a week, or more often if the weather is hot and dry. The soil should always be moist, but not waterlogged.

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