Using Calculo. How I can determine the pipeline route to use so that total cost

Question

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

Explanation / Answer

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)

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