Cable Connections

The local cable company has a main station located on a stretch of straight coastline. A small island lies twenty miles down the coast from the main office and five miles offshore. In order to supply service to the island, the cable company needs to run underground cable from the main station to a substation on the island. The cost for laying the cable is $30,000 per mile along the coast, but the cost for laying the cable under the ocean is$42,000 per mile. What is the minimum cost for connecting the two stations, and how can this be achieved?

2. Originally Posted by nelle87
Cable Connections

The local cable company has a main station located on a stretch of straight coastline. A small island lies twenty miles down the coast from the main office and five miles offshore. In order to supply service to the island, the cable company needs to run underground cable from the main station to a substation on the island. The cost for laying the cable is $30,000 per mile along the coast, but the cost for laying the cable under the ocean is$42,000 per mile. What is the minimum cost for connecting the two stations, and how can this be achieved?
Not sure why your heading says "radical equations" but this looks like a classic example for the Pathagorean Theorem.

Laying cable down the coastline for 20 miles @ $30,000/mi and under the ocean for 5 miles @$42,000 = $810,000 total cost. The hypotenuse of the right triangle formed by the 20 miles down the coast and 5 miles out to the island is about 20.62 miles. This is found by using the Pathagorean Theorem:$\displaystyle c^2=20^2+5^2\displaystyle c\approx20.62$So, the cost of going under the ocean directly from the main station would be$\displaystyle 20.62 \times 42000=865,852$So, it's$865,852 - $810,000 or$55,852 cheaper going the route of the two legs