optimization please help

Question

A luxury hotel group purchases a deserted island 3. 5 miles offshore and due south of an endangered bird nesting beach. The nearest power source is on land, 10 miles due east of the bird nesting beach. Surveying for electricity construction costs $250 per mile over the water and $150 per mile on the ground. As a surveyor, the cheapest price (in dollars) for which you can bill the job involves surveying above the water to a point inbetween the nesting beach and the power source, and then from the nesting beach to the power source. Find the least expensive price for which you can bill the job.

Answer 1

I have the problem worked out but there isn't a good way to post it here. Do you have a Wyzant account I could post it to?

Answer 2

the endangered beach seems to have no relevance here.

Cost = 250w+150l

for some point x between the beach and the power station, we have the distance from the island to x is sqrt(x^2+3.5^2) by pythagoreans theorem. the distance from x to the power station is just 10-x

so Cost = 250(sqrt(x^2+3.5^2)) + 150*(10-x)

Cost = 250sqrt(x^2+12.25) + 1500 -150x

Cost' = 500x(x^2+12.25)^(-1/2) -150

find min, set equal to 0. I leave the rest to you.