Calculus- area of a garden problem

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SUMMARY

The discussion focuses on optimizing the dimensions of a rectangular rose garden with an area of 1000m², surrounded by a brick wall on three sides and a fence on the fourth. The cost of the brick wall is $192/m, while the fencing costs $48/m. Participants emphasize the need to formulate the total cost as a function of the garden's length (L) and width (W) to minimize expenses effectively. The key equation to consider is the relationship between area and perimeter in the context of differing material costs.

PREREQUISITES
  • Understanding of basic calculus principles, particularly optimization.
  • Familiarity with area and perimeter formulas for rectangles.
  • Knowledge of cost functions and how to formulate them based on dimensions.
  • Ability to solve equations involving multiple variables.
NEXT STEPS
  • Learn how to derive cost functions from geometric constraints.
  • Study optimization techniques in calculus, specifically for functions of two variables.
  • Explore real-world applications of calculus in minimizing costs in construction projects.
  • Investigate methods for solving constrained optimization problems.
USEFUL FOR

Students studying calculus, particularly those tackling optimization problems, as well as individuals interested in practical applications of mathematical concepts in construction and landscaping.

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Homework Statement


A rectangular rose garden will be surrounded by a brick wall on three sides and a fence on the fourth side. The area of the garden will be 1000m2. The cost of the brick wall is $192/m. The cost of the fencing is $48/m. Find the dimensions of the garden so that the cost is a minimum. [domain and test not needed]


Homework Equations



So I know A = 1000m2 and A=lw

The Attempt at a Solution


My question is, how do I do this when the sides are different due to the materials used in building them? It's not like a question where you fence in three sides with the same stuff and just optimize costs...I'm very slow at calculus, please explain details! I really appreciate this.
 
Physics news on Phys.org
You want to think about the perimeter and its cost. Start by writing a formula for the cost:

Cost = some function of L and W.

That's what you want to minimize.
 

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