NOTE: USE LINGO ONLY!

2. (20 marks) A mining company has four mines located only a few kilometres apart. At 500 metres below the surface of the earth, they wish to build a tunnel system to connect these four mines. The most convenient points for these connections are at reference points (100, 2300), (300, 400), (3700, 1800), and (4100, 600). where (a,b) is a metres east and b metres north of a common reference point. The company wishes to determine where the connecting tunnels should be made. This is not like the three-point problem, with one central point to be found. For you own benefit, draw a picture and see how you would connect these points. For help, look at the Steiner tree Wikipedia article, found here. See the picture of the four-point solution. (a) Give the algebraic model of this problem. (b) Solve this model using LINGO or the Excel Solver. (c) State the solution in words