The state of massachusetts established a clearinghouse system, the commonwealth health insurance connector, which facilitated the buying, selling and administration of affordable, quality private insurance coverage for employers of 50 or fewer employees.

Centerville is the headquarters of greedy cablevision inc. the cable company is about to expand service to two nearby towns, springfield and shelbyville. there needs to be cable connecting centerville to both towns. the idea is to save on the cost of cable by arranging the cable in a y-shaped configuation. centerville is located at ( 12 , 0 ) (12,0) in the x y xy-plane, springfield is at ( 0 , 4 ) (0,4), and shelbyville is at ( 0 , − 4 ) (0,-4). the cable runs from centerville to some point ( x , 0 ) (x,0) on the x x-axis where it splits into two branches going to springfield and shelbyville. find the location ( x , 0 ) (x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. justify your answer.