Ask Question
20 February, 19:20

A fence must be built to enclose a rectangular area of 20 comma 000 ftsquared. fencing material costs $ 2 per foot for the two sides facing north and south and $4 per foot for the other two sides. find the cost of the least expensive fence.

+3
Answers (1)
  1. 20 February, 21:01
    0
    The first thing we should do is write the functions.

    For the area we have:

    A = w * h = 20000 feet ^ 2

    The price is:

    Cost = (4 * 2 * h + 2 * 2 * w)

    Substitute for h ::

    C (w) = (4 * 2 * (20,000 / w) + 2 * 2w)

    Rewrite we have:

    C (w) = 160,000 / w + 4w

    Take the derivative:

    C ' (w) = 160000 (-1 / w ^ 2) + 4

    We equal zero and clear w:

    0 = 160000 (-1 / w ^ 2) + 4

    160000 / w ^ 2 = 4

    w ^ 2 = 40000

    w = 200 (approximately)

    width = 200 ft; so cost is 2 * ($ 4) 200 = $ 1600

    height = 20000/200 = 100 ft; so cost is 2 ($ 2) 100 = $ 400

    Total cost = $ 2000

    Answer:

    The cost of the least expensive fence is:

    Total cost = $ 2000
Know the Answer?