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Calculus- area of a garden problem

  1. Apr 3, 2010 #1
    1. The problem statement, all variables and given/known data
    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]

    2. Relevant equations

    So I know A = 1000m2 and A=lw

    3. 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.
  2. jcsd
  3. Apr 3, 2010 #2


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    Science Advisor
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    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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