The Arctic Oil Company has recently drilled two new wells in a remote area of Alaska. The company is planning to install a pipeline to carry the oil from the two new wells to a transportation and refining (T&R) center. The locations of the oil wells and the T&R center are summarized in the following table. Assume a unit change in either coordinate represents 1 mile.
X Coordinate Y Coordinate
Oil Well 1 50 150
Oil Well 2 30 40
T&R Center 230 70
Installing the pipeline is a very expensive undertaking, and the company wants to minimize the amount of pipeline required. Because the shortest distance between two points is a straight line, one of the analysts assigned to the project believes that a separate pipe should be run from each well to the T&R Center. Another alternative is to run separate pipes from each well to some intermediate substation where the two lines are joined into a single pipeline that continues on to the T&R center. Arctic Oil's Management wants to determine which alternative is best. Furthermore, if using the intermediate substation is best, management wants to determine where this station should be located.
a. Create a spreadsheet model to determine how many miles of pipeline Arctic Oil must install if it runs separate pipelines from each oil well to the T&R center. How much pipe will be needed? Use Solver.
b.If Arctic Oil wants to build a substation, where should it be built? How much pipe is needed for this solution? Use Solver.
c. Which alternaive is best?
d. Suppose the substation cannot be built within a 10-mile radius of the coordinates X=80, Y=95. (Assume the pipeline can run through this area, but the substation cannot be built in this area.) What is the optimal location of the substation now, and how much pipe will be needed? Use Solver.