In the following diagram, S represents the position of a power relay station loc

Question

In the following diagram, S represents the position of a power relay station located on a straight coastal highway, and M shows the location of a marine biology experimental station on an island. A cable is to be laid connecting the relay station with the experimental station. The cost of running the cable on land is $4.00/running foot and the cost of running cable under water is $6.50/running foot.

Find an expression in terms of x that gives the total cost of laying the cable.
C(x) =    

What is the total cost when x = 1500? When x = 3000? (Round your answers to the nearest cent.)

Explanation / Answer

C(x) = (10000-x)*4 +(sqrt(x^2+ 3000^2))*6.5

x=1500 ==>c(x)= (10000-1500)*4 +(sqrt(1500^2+ 3000^2))*6.5 =55802$

x=3000 ==>c(x)= (10000-3000)*4 +(sqrt(3000^2+ 3000^2))*6.5 =55572$

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