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Math Help - Optimization Help Please!

  1. #1
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    Optimization Help Please!

    A fence is to enclose a rectangular area. One side is against a building so it needs no fence. This fencing costs $10/m. Inside the rectangular area there is a another fence at right angles to the building, costing $4/m. The total area enclosed is 12m^2. Find the dimensions for minimum cost. Include a second derivative test to show this is a minimum and include an answer with units and 3 sig. digits.

    Im having problems figuring out how to solve this problem. Help would be greatly appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by Hockey_Guy14 View Post
    A fence is to enclose a rectangular area. One side is against a building so it needs no fence. This fencing costs $10/m. Inside the rectangular area there is a another fence at right angles to the building, costing $4/m. The total area enclosed is 12m^2. Find the dimensions for minimum cost. Include a second derivative test to show this is a minimum and include an answer with units and 3 sig. digits.

    Im having problems figuring out how to solve this problem. Help would be greatly appreciated. Thanks!

    let x = fence distances perpendicular to the bldg

    y = fence distance parallel to the bldg

    xy = 12

    cost, C = 10(2x+y) + 4x

    using the area equation, solve for one of the variables in terms of the other (either x or y, your choice) , then substitute into the cost equation to get cost in terms of a single variable ... then do the calculus.
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