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Math Help - Optimization

  1. #1
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    Optimization

    A fence is to be made to enclose three sides of a rectangular area beside a river. The river forms the fourth side of the enclosure. This fence costs $30/metre. The enclosure is divided in half by another fence at right angles to the river. This fence costs $20/metre. The area to be enclosed is 500m^2. Find the dimensions for minimum cost of fencing.

    Please provide full solution. Thanks.
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  2. #2
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    Quote Originally Posted by meli3000 View Post
    A fence is to be made to enclose three sides of a rectangular area beside a river. The river forms the fourth side of the enclosure. This fence costs $30/metre. The enclosure is divided in half by another fence at right angles to the river. This fence costs $20/metre. The area to be enclosed is 500m^2. Find the dimensions for minimum cost of fencing.

    Please provide full solution. Thanks.
    C = 30x + 30w + 30x + 20x = 80x + 30w .... (A)

    A = wx \Rightarrow 500 = wx \Rightarrow w = \frac{500}{x} .... (B)

    Substitute equation (B) into equation (A) and then use calculus to find the value of x that gives a minimum of C.

    Substitute your answer for x into equation (B) to get the value of w.
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