OR확정-2017-중간고사 문제 해답.docx - 1 OR Deterministic Model 2017(Midterm Exam ID Number Name 2017 10.25(Wed < Full Credit 140 Pts 6

OR확정-2017-중간고사 문제 해답.docx - 1 OR...

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OR Deterministic Model 2017 (Midterm Exam.) 2017. 10.25 (Wed.) ID Number ( ), Name ( ) < Full Credit: 140 Pts, 6 Problems, 6 pages, 90 Minutes allowed > You may write your answers on the space below. If needed, use the back side of the page. 주의 : 스테이플 묶음을 뜯지 마시오 . 지면이 부족할 경우 해당문제의 뒷면을 이용하시오 . 1. (20 Pts) For the linear programming problem, the optimal solution was obtained using the graph as follows. (Text 2.2 example problem). The objective function is Max z = 5 x 1 + 4 x 2 . 선형계획법 문제에 대해 그래프를 이용하 여 다음과 같이 최적해를 구하였다 . (Text 2.2 예제문제 ). 목적함수는 Max z = 5 x 1 + 4 x 2 이다 . Suppose that s 1, ,s 2 , s 3 ,s 4 are the slack variables added to the constraint 1,2,3,4, respectively to make the standard type . 제약조건 1,2,3,4 를 표준형으로 만들기 위하여 추가한 여유변수 (Slack Variable) 을 각각 s 1 ,s 2 ,s 3 ,s 4 라고 하자 . (a) The feasible region is determined by the six extreme points of A, B, C, D, E, and F. Which constraint creates vertex E? 가능해의 영역 (Feasible Region) A,B,C,D,E,F 6 개 꼭지점 (Extreme Point) 에 의해 결정된다 . 어느 제약조건이 꼭지점 E 를 만들어내는가 ? 3 and 4 (b) When the solution is obtained by the simplex method, each step moves along the extreme points to find the optimal solution. In the step corresponding to vertex B, what are the basic variables and the nonbasic variables? 심플렉스 해법 으로 해를 구하면 각 단계는 꼭지점을 따라 이동하여 최적해를 구하게 된다 . 꼭지점 B 해당하는 단계에서 기저변수 (Basic Variable) 와 비기저변수 (Nonbasic Variable) 는 무엇이 며 이들의 값을 각각 구하시오 . Basic Variable ; x 1 = 4 ,s 2 = 2 ,s 3 = 5, s 4 = 2 Non-Basic Variable ; s 1 = 0 , x 2 = 0 (Extreme Point B is made by constraints 1 and 6, hence corresponding slack variable s 1 = 0 and obviously x 2 = 0 , which are non-basic variables. By plugging these values results in x 1 = 4 ,s 2 = 2 ,s 3 = 5, s 4 = 2 ) 2. (30 Pts.) Aircrafts need to be assigned to the four routes operated by the airline. A total of 23 1
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aircrafts are in operation, each of which has 50, 30, or 20 seats for Type 1,2, and 3, respectively. The number of expected passengers per route is given in the table below (1,000, 2,000, 900, 1,200), and the number of trips allowed for each type of aircraft is given for each route as the table below. In addition, the operating costs incurred for each trip are given as shown in the second table below. Failure to accommodate all expected passengers per day will result in loss cost (4, 5, 5, 7) units per passenger for route (1, 2, 3, 4), respectively. Define the appropriate decision variables, and complete formulation for the allocation of aircraft by route to minimize the sum of the operating cost of aircraft operation and the loss cost for unacceptable passengers. 항공사가 운영하는 4 개의 항로 (Route) 에 대 해 항공기 (Aircraft) 를 배정하고자 한다 . 보유하고 있는 항공기는 세가지 타입 (Type) 으로 각각 (5,8,10) 대로서 총 23
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