1989美国数学建模数学竞赛试题及翻译

1989 MCM A: The Midge Classification Problem
Two species of midges, Af and Apf, have been identified by biologists Grogan and Wirth on the basis of antenna and wing length (see Figure 1). It is important to be able to classify a specimen as Af of Apf, given the antenna and wing length. Given a midge that you know is species Af or Apf, how would you go about classifying it?
Apply your method to three specimens with (antenna, wing) lengths
(1.24,1.80),(1.28,1.84),(1.40,2.04).
Assume that the species is a valuable pollinator and species Apf is a carrier of a debilitating disease. Would you modify your classification scheme and if so, how? 两种蠓Af和Apf已由生物学家W.L.Grongan和W.W.Wirth（1981年）根据他们的触角长和翼长加以区分。

根据触角的长和翼长将标本分类是很重要的。

1、给你一只Af或者Apf的蝶，你怎样对它进行分类呢?
2、用你的方法将翅膀、触角的长度分别为（1.24，1.80）（1.28，1.84）（1.40，2.04）的三个标本分类。

3、假设Af这个种类的是宝贵的传粉益虫，Apf确是传递令人衰弱的疾病的载体。

你是否会修改你的分类方法，如果要，怎样修改？
1989 MCM B: Aircraft Queueing
A common procedure at airports is to assign aircraft (A/C) to runways on a
first-come-first-served basis. That is, as soon as an A/C is ready to leave the gate (“push-back”), the pilot calls ground control and is added to the queue. Suppose that a control tower has access to a fast online database with the following information for each A/C:
the time it is scheduled for pushback;
the time it actually pushes back; the number of passengers who are scheduled to make a connection at the next stop, as well as the time to make that connection; and the schedule time of arrival at its next stop Assume that there are seven types of A/C with passenger capacities varying from 100 to 400 in steps of 50. Develop and analyze a mathematical model that takes into account both the travelers' and airlines' satisfaction.
机场通常是用“先来后到”的原则来分配飞机跑道，即当飞机备好离开登机口时，驾驶员电告地面控制中心，加入等候跑道的队伍。

假设控制塔可以从快速联机数据库中得到每架飞机的如下信息：
1、预定离开登机口的时间；
2、实际离开登机口的时间；
3、机上乘客人数；
4、预定在下一站转机的人数和专辑的时间；
5、到达下一站的预定时间。

又设共有七种飞机，载客量从100人起以50人递增，载客最多的是一种400人、试开发和分析一种能使乘客和航空公司双方满意的数学模型。

本题是有纽约市立大学约克学院的Joseph Malkevitch提供的。