Well, that's quite a pipe dilemma! Let me think... If the resort wants to minimize construction costs, they should aim to balance the cost of laying pipe on land with laying pipe in water.
Since it costs 1.4 times as much money to lay pipe in water, we can assume that laying pipe in water is the more expensive option. So, the resort should try to minimize the distance of the pipe in water.
Now, the key here is to find the perfect sweet spot along the shoreline. If the pipe reaches land too close to the island, they would have to lay more pipe on land, which would be cheaper. If the pipe reaches land too close to the source of fresh water, they would have to lay more pipe in water, which would be more expensive.
Let's do some calculations. The total cost of pipe construction can be represented by the equation:
Cost = Cost of pipe on land + Cost of pipe in water
Since the cost of pipe in water is 1.4 times the cost of pipe on land, we can write:
Cost of pipe in water = 1.4 * Cost of pipe on land
Now, let's represent the distance from P where the pipe reaches land as x. The distance from P to the source of fresh water is given as 10 miles. So, the distance of pipe in water would be 6 miles - x (since it is exactly 6 miles from P to the island).
Finally, we can substitute these values into our equations:
Cost = Cost of pipe on land + Cost of pipe in water
Cost = Cost of pipe on land + 1.4 * Cost of pipe on land
Cost = 2.4 * Cost of pipe on land
So, we want to minimize the total cost, which means we need to minimize the Cost of pipe on land. This would happen when the distance from P where the pipe reaches land, x, is maximized.
Therefore, the pipe from the island should reach land as close to the source of fresh water as possible, 10 miles down the shoreline from P. This way, there would be no cost for laying pipe in water, and the cost would be minimized.
Voila! The resort can save some serious construction costs by keeping the pipe out of the water. Just remember, in the piping world, dry land is always cheaper than diving into the deep blue sea!