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1、19852015年美国大学生数学建模竞赛题目集锦目录1985 MCM A: Animal Populations31985 MCM B: Strategic Reserve Management31986 MCM A: Hydrographic Data41986 MCM B: Emergency-Facilities Location41987 MCM A: The Salt Storage Problem51987 MCM B: Parking Lot Design51988 MCM A: The Drug Runner Problem51988 MCM B: Packing Railro
2、ad Flatcars61989 MCM A: The Midge Classification Problem61989 MCM B: Aircraft Queueing61990 MCM A: The Brain-Drug Problem61990 MCM B: Snowplow Routing71991 MCM A: Water Tank Flow81991 MCM B: The Steiner Tree Problem81992 MCM A: Air-Traffic-Control Radar Power81992 MCM B: Emergency Power Restoration9
3、1993 MCM A: Optimal Composting101993 MCM B: Coal-Tipple Operations111994 MCM A: Concrete Slab Floors111994 MCM B: Network Design121995 MCM A: Helix Construction131995 MCM B: Faculty Compensation131996 MCM A: Submarine Tracking131996 MCM B: Paper Judging131997 MCM A: The Velociraptor Problem141997 MC
4、M B: Mix Well for Fruitful Discussions151998 MCM A: MRI Scanners161998 MCM B: Grade Inflation171999 MCM A: Deep Impact171999 MCM B: Unlawful Assembly182000 MCM A: Air Traffic Control182000 MCM B: Radio Channel Assignments192001 MCM A: Choosing a Bicycle Wheel202001 MCM B: Escaping a Hurricanes Wrath
5、 (An Ill Wind.)212002 MCM A: Wind and Waterspray232002 MCM B: Airline Overbooking232003 MCM A: The Stunt Person242003 MCM B: Gamma Knife Treatment Planning242004 MCM A: Are Fingerprints Unique?252004 MCM B: A Faster QuickPass System252005 MCM A: Flood Planning262005 MCM B: Tollbooths262006 MCM A: Po
6、sitioning and Moving Sprinkler Systems for Irrigation272006 MCM B: Wheel Chair Access at Airports282007 MCM A: Gerrymandering292007 MCM B: The Airplane Seating Problem292008 MCM A: Take a Bath302008 MCM B: Creating Sudoku Puzzles302009 MCM A: Designing a Traffic Circle302009 MCM B: Energy and the Ce
7、ll Phone302010 MCM A: The Sweet Spot322010 MCM B: Criminology322011 MCM A: Snowboard Course332011 MCM B: Repeater Coordination332012 MCM A: The Leaves of a Tree332012 MCM B: Camping along the Big Long River342013 MCM A: The Ultimate Brownie Pan342013 MCM B: Water, Water, Everywhere352014 MCM A: The
8、Keep-Right-Except-To-Pass Rule352014 MCM B: College Coaching Legends362015 MCM A: Eradicating Ebola362015 MCM B: Searching for a lost plane361985 MCM A: Animal PopulationsChoose a fish or mammal for which appropriate data are available to model it accurately. Model the animals natural interactions w
9、ith its environment by expressing population levels of different groups in terms of the significant parameters of the environment. Then adjust the model to account for harvesting in a form consistent with the actual method by which the animal is harvested. Include any outside constraints imposed by
10、food or space limitations that are supported by the data.Consider the value of the various quantities involved, the number harvested, and the population size itself, in order to devise a numerical quantity that represents the overall value of the harvest. Find a harvesting policy in terms of populat
11、ion size and time that optimizes the value of the harvest over a long period of time. Check that the policy optimizes that value over a realistic range of environmental conditions.1985 MCM B: Strategic Reserve ManagementCobalt, which is not produced in the US, is essential to a number of industries.
12、 (Defense accounted for 17% of the cobalt production in 1979.) Most cobalt comes from central Africa, a politically unstable region. The Strategic and Critical Materials Stockpiling Act of 1946 requires a cobalt reserve that will carry the US through a three-year war. The government built up a stock
13、pile in the 1950s, sold most of it off in the early 1970s, and then decided to build it up again in the late 1970s, with a stockpile goal of 85.4 million pounds. About half of this stockpile had been acquired by 1982.Build a mathematical model for managing a stockpile of the strategic metal cobalt.
14、You will need to consider such questions as: How big should the stockpile be? At what rate should it be acquired? What is a reasonable price to pay for the metal?You will also want to consider such questions as: At what point should the stockpile be drawn down? At what rate should it be drawn down?
15、At what price is it reasonable to sell the metal? How should it be allocated?Useful Information on CobaltThe government has projected a need ot 25 million pounds of cobalt in 1985.The U.S. has about 100 million pounds of proven cobalt deposits. Production becomes economically feasible when the price reaches $22/lb (as occurred in 1981). It takes four years to get operations rolling, and thsn six million pounds per year can be produced.In 1980, 1.2 million pounds of cobalt were recycled, 7% of total consumption.1986 MCM A: Hydrographic DataThe table be
