Answer Happy

• The cost per foot of pipe installed is $7.80 over land, and $10.50 over swamp. • A maximum of two elbow joints may be used. These can be fabricated with any desired angle measure. This means that your pipe must go in straight line segments, and you can have a maximum of three attached line segments by using your two elbow joints. • You can also choose to use 0 or 1 elbow joints. 1. To help you envision what needs to be done for this modeling project, begin by modeling the swamp with a rectangle. Consider the different possible routes for laying the pipe - you could go around the swamp, either above or below, you could connect in a straight line directly across the swamp, or you could lay it along the shore for some distance, and then use an elbow joint to angle across the swamp to the other point. 2. Express the various potential routes geometrically (draw diagrams), then express the costs of the various potential routes algebraically (as a function of some variable, like the distance from the starting point to the elbow joint, clearly defining your variable), then apply the techniques of calculus to minimize this function. Note that the routes around the swamp will have a constant cost. 3. After familiarizing yourself with this approach using a simple geometric model of the swamp, you must then provide a more accurate model using a more trapezoidal approximation for the swamp, and follow the same procedure as above. Finally, you should present your models and your recommendations to the company in the form of a report. 4. Just days before you are planning to present you proposal to the company, they tell you that the cost of the piping has increased by $3 per foot, which will affect the cost per foot both over dry land and over swamp. Use the same geometric model that you used in part 2, and recalculate the optimum route. 5. Write up your report as if you were writing to the supervisor, explaining the best route, and why it is best. Grading will be based upon reasonableness of the model chosen,