Using Calculo How I can determine the pipeline route to use

Using Calculo. How I can determine the pipeline route to use so that total cost is minimized (The cheaper one) From A to B in the given map. Scale 1 cm = 100 ft. and the distance between A and B is 825.5feet. We need to consider the following below (Map is given for reference below)

\"The instructor just gave me the following Hint: You probably want to represent the wetland with a simple geometric figure, like a rectangle, and work with it from that perspective, but the choice of how to do themodel is up to you.\"

Straight, two-inch coated pipe must be used at a cost of $15.00/foot.

A maximum of two elbow joints may be used. Any angle and cost $550.00 a piece.

In crossing normal terrain, installation cost is $20.00/foot, but in wetland area requires the use of a Track Hoe. Cost of $180/hour. In a 10 hour day the Track Hoe can usually dig approximately 300

1 scale 1 cm= 100 ft ROAD AK.ua da.da A98

Solution

The minimum distance between any two points is straight line.

But here as in the middle it is wet land we can use right triangle to join A and B

From A draw a horizontal pipe and B draw a vertical pipe with one elbow joint.

The length of the pipe = Ac^2+CB^2 where C is the joint.

Total cost = 20(length) + 180(300)AC/10+cost of elbow

= 20(length)+180(300)/AC+550+ labour cost (180* no of hours)