How Do You Minimize Cost While Building a Rectangular Enclosure?

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  • #1
eownby77
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The manager of a department store wants to build a 600 square foot rectangular enclosure on the store's parking lot in order to display some equipment. Three sides of the enclosure will be built of redwood fencing at a cost of $7 per running foot. The fourth side will be built of cement blocks at a cost of $14 per running foot. Find the dimensions of the enclosure that will minimize the total cost of the building materials.

I started out with (2x)(2y) = 600 for the area. Solved for y to get y= 300/2x. What I don't get is that there are going to be two side lengths, and 3 of them will cost less than one. Would I maximize the dimensions to find the minimum costs? You can't just set it up with 3 sides being the same, because then it wouldn't be a rectangle.

The first derivative I think is 2 - 300/x^2. Critical points: d.n.e. at x=0, after setting 2-300/x^2, x= square root of 150

I don't know how to find the domain, or where I should go from there.
 
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  • #2
eownby77 said:
The manager of a department store wants to build a 600 square foot rectangular enclosure on the store's parking lot in order to display some equipment. Three sides of the enclosure will be built of redwood fencing at a cost of $7 per running foot. The fourth side will be built of cement blocks at a cost of $14 per running foot. Find the dimensions of the enclosure that will minimize the total cost of the building materials.

I started out with (2x)(2y) = 600 for the area. Solved for y to get y= 300/2x. What I don't get is that there are going to be two side lengths, and 3 of them will cost less than one. Would I maximize the dimensions to find the minimum costs? You can't just set it up with 3 sides being the same, because then it wouldn't be a rectangle.

The first derivative I think is 2 - 300/x^2. Critical points: d.n.e. at x=0, after setting 2-300/x^2, x= square root of 150

I don't know how to find the domain, or where I should go from there.

1) Define your variables, including units.
2) Write an expression for area in terms of the variables.
3) Write an expression for cost in terms of the variables.
4) Think about what you need to do to minimize something.

RGV
 

FAQ: How Do You Minimize Cost While Building a Rectangular Enclosure?

1. What is applied optimization?

Applied optimization is a branch of mathematics that deals with the process of finding the best possible solution to a problem, given a set of constraints. It involves using mathematical techniques and algorithms to maximize or minimize a specific objective function.

2. What are some real-life applications of applied optimization?

Applied optimization has a wide range of applications in various fields such as engineering, economics, finance, and computer science. Some common examples include optimizing production processes, designing efficient transportation routes, and maximizing profits in a business.

3. How is applied optimization different from theoretical optimization?

Theoretical optimization focuses on developing mathematical models and proving theorems about optimal solutions, while applied optimization involves using these models and techniques to solve real-world problems. Applied optimization also takes into account practical considerations such as data limitations and computational efficiency.

4. What are some common techniques used in applied optimization?

Some common techniques used in applied optimization include linear programming, nonlinear programming, dynamic programming, and genetic algorithms. These techniques can be applied to a wide range of problems and are often combined to find the most effective solution.

5. How can I get help with applied optimization?

If you are struggling with applied optimization, you can seek help from a tutor, attend workshops or online courses, or consult with a professional in the field. Many universities also offer resources such as study groups and tutoring services to assist students with applied optimization.

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