A square plot of ground 100 feet on a side has vertices labeled A, B, C, D clock

Question

A square plot of ground 100 feet on a side has vertices labeled A, B, C, D clockwise. Pipe is to be laid in a straight line from A to a point P on BC (P may be one of the vertices), and from there to point C. The cost of laying the pipe is $20 per foot if it goes through the lot (since if must be laid underground), and $10 per foot if it is laid along one of the sides of the square. What is the minimum cost for paying the pipe and how should the pipe be laid?

    a)        1. Solve this problem by the Trigonometric approach.

    b)        2. Solve this problem by the traditional

Explanation / Answer

let x be the distance from P to C
x=100 then cost = 2000

if x < 100 then
cost = sqrt(10000+x*x) * 20 + (100-x) * 10
minimum at x = 57.735
cost = 2732.05

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