Gr 12 Calc: Optimization problem/min cost

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SUMMARY

The discussion focuses on optimizing the dimensions of a rectangular garden to minimize fencing costs while maintaining an area of 432 m². The homeowner will share the cost of the fence with the neighbor, who will pay for half of the shared side. The cost of fencing is set at $45 per meter. The key to solving the problem lies in establishing a cost function based on the dimensions of the garden and using calculus to find the minimum cost.

PREREQUISITES
  • Understanding of basic algebra and geometry for calculating area and perimeter
  • Knowledge of optimization techniques in calculus, specifically finding minima
  • Familiarity with cost functions and their applications in real-world scenarios
  • Ability to interpret and create diagrams to visualize mathematical problems
NEXT STEPS
  • Learn how to set up and solve optimization problems using calculus
  • Study the concept of cost functions and their derivation
  • Explore practical applications of optimization in real estate and construction
  • Review examples of similar optimization problems in geometry
USEFUL FOR

This discussion is beneficial for high school students studying calculus, educators teaching optimization problems, and anyone interested in applying mathematical concepts to real-world scenarios such as cost management in construction projects.

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Homework Statement



A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence
  1. What should the dimensions of the garden be if the area is 432 m^2 and the homeowner would like to keep his share of the cost to a minimum? Include a diagram.
  2. At $45/m, what is the homeowner’s cost? What is the neighbour’s cost?

Homework Equations

The Attempt at a Solution


[/B]
My diagram https://i.imgur.com/4Pvpxg3.jpg

From there I know that I need to find what y equals but this is where I get stuck. After I find y I need to find
the side of the fence that is shared with the neighbour. Then I can set up a cost function. I haven't done any questions like this before so I am struggling. I guess I just need some help setting up the problem. Thanks
 
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Specter said:
Then I can set up a cost function
Make an attempt... you know the price per meter, you want to know the cost, so you'll need ... :rolleyes:

Oh, and read the guidelines, about this required attempt and about posting pictures directly, not on some temporary cookiemonster
 

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