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University of Waterloo
Combinatorics and Optimization
CO 250
Christine Dupont

Assignment 5 Due: Wednesday April 3 at the BEGINNING of class 1. A power plant has two boilers, which produce steam, and two turbines, which produce power from steam. The following two tables give the speci▯cations of the boilers and the turbines. The ▯rst table lists the ▯xed cost incurred in operating a boiler, the cost of producing a ton of steam on each boiler. The ▯rst table also lists the range in which the steam produced from the boiler must lie, if the boiler is operated. The second table lists the range of the amount of steam that can be processed on a turbine, the power generated by the turbine, and the cost of processing steam on the turbine. Boiler Steam produced Fixed Cost Steam Production Cost (range in tons) To Operate (per ton) 1 [600, 1200] 1100 11 2 [400, 800] 850 9 Turbine Steam Capacity Power Generated Processing Cost (range in tons) (kWh/ton) (per ton) 1 [500, 700] 5 3 2 [550, 950] 6 4 To prevent damage to any equipment, any steam produced by the boilers must be processed by the turbines. Write an integer program to minimize the cost of generating exactly 6400 kWh or power. 2. The Waterloo Maple Leafs is a local hockey team that has asked you to decide who should be playing during a power play. There are 10 members that can play positions Winger (W), Center (C), and/or Defense (D). The starting lineup needs exactly 5 play- ers where the number of players that can play each position is at least 2 for Winger, at least 1 for Center, and at least 1 for Defense (you can have a player represent more than one of these required positions). Players on the team are also ranked on their scoring ability from 1 to 5 (5 being the best). Each player’s number, position, scoring ability is listed below: Player # Player Positions Scoring Ability 1 W. Belak W, D 2 2 T. Bozak C 4 3 C. Franson D 3 4 M. Frazer D 1 5 N. Kadri W, C 5 6 P. Kessel W 5 7 J. McClement W, C 3 8 C. Orr W 1 9 D. Phaneuf D 3 10 D. Steckel W, C 1 There are some addition issues that need to be taken into account: ▯ D. Steckel doesn’t like J. McClement. To prevent any issues, the coach wants if D. Steckel plays, then J. McClement to not play. ▯ The
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