PAPUA NEW GUINEA MINING COMPANY The Papua New Guinea Mining Company (PNGM Co.) mines gold, silver, and copper from four sites on the island of New Guinea. The mining activities takes place in the highlands, which provide no major sources of water. Water is an essential ingredient in the bacterial leaching. done at three sites at lower elevations. Currently only pilot operations are being conducted while the ore sites are surveyed, and final planning is done. The overall scheme is to extract the ore and transport it to one of the leaching sites. There, the metals will be separated from the nonmetallic compounds, using several strains of Thiobacillus. The concentrated metallic "soup" will then be transported to the port facility in Port Moresby, loaded onto tankers, and shipped to Australia to be refined and smelted. Papua New Guinea is an extremely undeveloped place with few roads. Except for the port facility, the PNGM Co. sites are in remote jungle or mountain locations unconnected by roads or navigable waterways. Three major transportation projects are being considered. One is to construct a railway connecting the various sites. The railway may just connect the mines to the leaching sites, or it may also connect the latter to the port. If the shorter rail option is adopted, the enriched slurry will be routed to port through pipelines. A series of aqueducts must also be constructed to connect the leaching sites to water sources. The final railroad bed and pipeline choices will be based on the distances separating the various sites. These are shown in Table 1, in which the distances (in kilometers) between neighboring sites are listed as candidate routes. The water sources include two lakes - Lake Amau (LA) and Lake Karena (LK) - two rivers - the Mor (RM) and the Vanapa (RV) - and one well (W). The maximum possible flows__D'__ ___D __'__ __ _'____ ____'_ ___'__' The water sources include two lakes Lake Amau (LA) and Lake Karena {LK} two rivers the Mor {Rh-'1) and the Vanapa (RV) and one well (W). The maximum possible ows {millions of cubic liters per hour) are shown in Table 2. along with the maximum required or available. Chief engineer Rov Youngblatt has selected a special gondola car for hauling ore to the leaching sites. 'When empty. these cars can accommodate a large removable rubber bladder which will contain the metalenriched liquid drawn from the leaching sites. so the same cars can be used to move the liquid to port. Rail cars with empty bladders can then be returned to the leaching sites. where the bladders are removed before the emptyr cars are returned to the mines. In terms of number of lled gondola cars. the daily ore volume limitations listed in Table 3 apply to the shipments from the mines. For mo st of the routes from mines to leaching sites. there is no lower bound on the number of gondola carloads. Generally. at most 40 carloads can be shipped. There are several exceptions. The maximum number of carloads is 30 over route AD; 20 over route (3D. and ID over route E G. The minimum number of carloads is 20' each over routes AG and CG. 'When each ore car is emptied at the leaching site. it is recongured as a gondolabladder car. Thus. every car entering a leaching site full of ore leaves it loadedwith a full bladder of metallic soup pumped from the holding ponds. The carload limitations listed in Table 4 apply to shipments from leaching sites to the port. Table 1. Site Distances Site A B C D H A (mine) if 55 50 60 B(leaching) - 25 C(mine) - 30 D(leaching) E(mine) 15 80 F(mine) 65 70 G(leaching) 1 - 75 H(port )30 Table 2. Maximum Possible Flows, Availabilities, and Requirements Leaching Sites Water Source B D G Available LA 2 0 LK 3 0 4 RM 0 6 RV 4 6 W Maxim um 10 10 10Table 3. Ore Quantity Limitations Site Lower Bound Upper Bound 0 50 C O 60 E O 80 O 70 Table 4. Carload Limitations Site Lower Bound Upper Bound B 20 80 D 30 80 G 40 100 Questions 1. Each site will be connected to at least one other site by the railroad. The rail links will traverse some subset of the linkages in Table 1. a. Determine the minimum track length and the corresponding routes and spurs that will be needed if the port and leaching sites are included. b. Repeat part (a), leaving out the linkages to the port. 2. Determine the minimum pipeline length for connecting the port to the leaching sites, leaving out the linkages to mine sites A, C, and F. Prune any legs ending at a mine site. 3. Find the aqueduct volumes that will maximize the flow from the water sources to the leaching sites