Final answer:
To minimize the cost, the fiber optic cable should be laid perpendicularly from point S to the closest point on the direct path to the destination, then along the less costly route, either underground along the shore or to the broadcast station B, to reduce the more expensive underwater segment.
Step-by-step explanation:
To minimize the cost of laying fiber optic cable given that the underwater installation is three times costlier than underground, we have to consider the least expensive path. We do not have the specific diagram or distances to make a precise calculation, but generally, a direct path (Option a or c) might seem shorter, but if the underwater distance is longer than the shore path, it can result in higher costs due to the multiplication factor of underwater installation (three times the cost). Conversely, perpendicularly extending from point S to the nearest point on the direct route to the destination (whether the shore for Option b or the broadcast station B for Option d), and then running the cable along the less expensive route (underground along the shore), will tend to reduce the underwater segment and hence minimize the overall cost. A precise answer would require analyzing the specific geometry of the situation to calculate the shortest and least costly route.