Optimization question

[spooky]

An oil rig lies 20 km off the coast of Newfoundland. A town lies 80 km along the coast from the nearest point on land to the rig. A pipe is to be drilled from the rig to the town. The cost per km of the pipe under water is $2.5 million, but on land is $1.5 million. Find the route that results in the cheapest pipeline, and determine that lowest cost.

I would greatly appreciate if you guys could look over my solution

 

[blamocur]

Since we only spend limited amount of time on this forum we'll naturally give priority to requests which are easy to read and/or understand. I am sorry to say your handwritten solution does not fit that category

 

[Otis]

Hi spooky. Your general method is good, and your answers are correct.

Your work looks rushed and shows issues related to carelessness (eg: incorrect radical signs leading to incorrect radicands, extra algebraic steps, switching back and forth between rational and decimal forms, missing arithmetic operators, some illegible handwriting).

[imath]\;[/imath]