Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

PLEASE HELP me solve this calculus optimization word problem?

A cable television company is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides of Willow Creek, which is 100m wide. The company has to connect points P and Q with cable, where Q is on the north bank 1200m east of P. It costs $40/m to lay cable underground and $80/m to lay cable underwater. What is the least expensive way to lay cable?

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  • M3
    Lv 7
    9 years ago
    Favorite Answer

    A .. X .....................Q

    ...............................

    |...../

    |..../

    |.../

    |../

    | /

    |/.............................

    P

    AP = w = 100m

    AX = x

    k = ratio of underwater cost / underground cost = 2

    let angle APX = z

    working out optimal path will give sin z = 1/k which yields

    x = w/sqrt(k^2-1) = 100/sqrt 3 = 57.735 m <-----------

    note that the distance AQ doesn't figure in the solution !

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