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1 March, 11:34

Suppose a rectangular plot is to be fenced in, with the fencing on each of the four sides (labeled east, west, north, south) costing as follows: north: $4 per foot south: $5 per foot east: $3 per foot west: $5 per foot and the total cost of fencing is to be $700. What is the maximum area in ft2 of such a plot?

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  1. 1 March, 15:24
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    A = 1701,38 ft²

    Dimensions:

    x (north and south sides) = 38.89 ft

    y (east and west sides) = 43,75 ft

    Step-by-step explanation:

    North and south (sides of same length) equal "y" cost (4 + 5) = 4,5 $/ft²

    East and west (sides of same length) equal "x" cost (3 + 5) = 4 $ / ft²

    Equation of cost is

    C = Cost of (north + south) + Cost (east + west)

    C = 2 * 4,5 * x + 4*2 * y

    C = 9x + 8y

    700 = 9x + 8y ⇒ y = (700 - 9x) / 8

    A = x*y

    A (x) = x * (700 - 9x) / 8

    A (x) = (700 x - 9x²) / 8 A' (x) = (700 - 18 x) / 8 A' (x) = 0

    (700 - 18 x) / 8 = 0 ⇒ 700 - 18 x = 0 ⇒ x = 700/18

    x = 38.89 ft

    y = (700 - 9x) / 8 ⇒ y = 349.99 / 8 ⇒ y = 43.75

    And maximum ara is

    A = x*y A = 38.89 * 43.75 = 1701,38 ft²
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