The figure represents an oil pipeline network. The nodes represent pumping and/or receiving stations. The lengths in miles of the different segments of the network are shown on the respective ares. The bi-directional segments allow flows in both directions. The supplies at stations 1 and 3 are respectively 60 and 50 barrels per day. The demands at the stations 2 and 4 are respectively 85 and 25 barrels per day. Assume that the transportation cost per shipped barrel is proportional to the distance and we are interested in minimizing the total transportation cost. 3 15 16 2 7 A 40 10 12 6 5 50 Figure 1: Problem 1 (a) Optimize the transportation schedule (ie. write the problem that consists of an objective function and constraints). (b) Is this a linear or non-linear optimization problem? Please briefly explain