Question

A small resort is situated on an island off a part of the coast of Mexico that has a perfectly straight north-south shoreline. The point P on the shoreline that is closest to the island is exactly 6 miles from the island. Ten miles south of P is the closest source of fresh water to the island. A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between P and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 2.2 times as much money to lay pipe in the water as it does on land. How far south of P should Q be located in order to minimize the total construction costs?

Answer 1

To minimize the total construction costs, point Q should be located C/3.2 miles south of point P.

Step-by-step explanation:

In order to minimize the total construction costs, we need to find the location of point Q on the shoreline that is south of point P. Let's assume that the distance from P to Q is x miles.

Since it costs 2.2 times more to lay pipe in the water than on land, the cost of laying pipe in the water would be 2.2 times x, and the cost of laying pipe on land would be 1 times x (or just x). The total cost C can be expressed as:

C = 2.2x + x = 3.2x

To minimize the total cost, we need to find the value of x that minimizes C. Since x represents the distance from P to Q, it should be a positive value. We can divide both sides of the equation by 3.2 to get:

x = C/3.2

Therefore, the location of point Q should be located C/3.2 miles south of point P in order to minimize the total construction costs.

Answer 2

1.7*(x2+9)0.5+(10-x)=min

Also, the 2 is an exponent.