It is required to lay a cable from a point A on one side of the bank of a river 100m wide to a point B on the opposite bank 1500m downstream from the point C directly opposite A.(Assuming the river bank are parallel).What rout should be followed to minimize
The cost,if it costs $30.00 per meter to lay cable on land and $ 60.00 per meter to lay in the water?

Problems very similar to this one can be found by googling. This is a very cliché calculus problem. One can find it in some form or another online or in any calc book.

First, draw a picture. Note, there is a right triangle which the hypoteneuse represents the length of cable under water across the river. See it?

Let the portion along the bank, on land, be 1500-x.

The cost on land is 30(1500-x) and the cost underwater is 60\sqrt{x^{2}+100^{2}}

Then, the total cable cost will be C=30(1500-x)+60\sqrt{x^{2}+100^{2}}

This is what must be optimized to find the length across land and under the water. Differentiate, set to 0, and solve for x. Look at the diagram I have provided. See what is going on?