A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides is to be made of material that costs 3

Question

A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

in progress 0
2 weeks 2021-11-23T14:10:44+00:00 1 Answer 0

Answers ( )

    0
    2021-11-23T14:12:10+00:00

    Answer:

    Length of the rectangle = 9.58 feet and width = 27.14 foot

    Step-by-step explanation:

    Let the length of the rectangular area is = x feet

    and the width of the area = y feet

    Area of the rectangle = xy square feet

    Or xy = 260

    y = \frac{260}{x} ——-(1)

    Cost to fence the three sides = $3 per foot

    Therefore cost to fence one length and two width of the rectangular area

    = 3(x + 2y)

    Similarly cost to fence the fourth side = $14 per foot

    So, the cost of the remaining length = 14x

    Total cost to fence = 3(x + 2y) + 14x

    Cost (C) = 3(x + 2y) + 14x

    C = 3x + 6y + 14x

      = 17x + 6y

    From equation (1)

    C = 17x+\frac{260\times 6}{x}

    Now we take the derivative,

    C’ = 17 – \frac{1560}{x^{2} }

    To minimize the cost of fencing,

    C’ = 0

    17 – \frac{1560}{x^{2} } = 0

    \frac{1560}{x^{2} } = 17

    x^{2} =\frac{1560}{17}

    x=\sqrt{\frac{1560}{17} }

    x = 9.58 foot

    and y = \frac{260}{9.58}

    y = 27.14 foot

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )