Functions of several cariables - minimum cost

In summary, to minimize the cost of a closed rectangular box with a volume of 16 cu. ft, an equation can be written in terms of the three dimensions and using the fixed volume to eliminate one variable. Setting the partial derivatives of the cost with respect to the remaining two variables equal to zero will result in two equations that can be used to determine the dimensions of the box.
  • #1
glitchy
17
0
A closed rectangular bos with a volume of 16cu. ft is made from 2 kinds of materials. the top and bottom are made of material costing 10cents per square foot and the sides of the material costing 5censts per sqaure foot. what r the dimenstions of the box so that the cost of the materials is minimized.

How do I go about starting this.

I was able to solve a similar one regarding maximizing the volume of a box, nothing with cost though.

any help is appreciated.
 
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  • #2
Write an equation for the cost of the box in terms of the three dimensions. Use the fixed volume of the box to eliminate one of the variables. Then set the partial derivatives of the cost with respect to the two remaining variables equal to zero. The result should be two equations in two variables. Et voila.
 

1. What is the minimum cost function?

The minimum cost function is a mathematical function that calculates the lowest possible cost for a given set of variables. It is often used in optimization problems where the goal is to find the most efficient solution.

2. How is the minimum cost function calculated?

The minimum cost function is typically calculated using calculus, specifically the technique of partial derivatives. By taking the derivative of the function with respect to each variable and setting them equal to zero, the minimum cost can be found.

3. What are the variables that affect minimum cost?

The variables that affect minimum cost can vary depending on the specific problem. However, common variables include production costs, labor costs, material costs, and transportation costs.

4. Are there any limitations to using the minimum cost function?

Yes, there are limitations to using the minimum cost function. It assumes that the relationship between the variables and cost is linear, and it may not accurately capture real-world complexities. Additionally, it may not account for external factors that can affect costs.

5. How is the minimum cost function used in real-world applications?

The minimum cost function is used in a variety of industries, including manufacturing, logistics, and finance. It helps businesses make informed decisions about production, pricing, and resource allocation to minimize costs and maximize profits.

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