河海大学文天学院运筹学考试试题.doc

2008-2009学年第一学期《运筹学》期末试卷
(经济学专业06级)
Class　　　　 IN Number　　　　　　 Name　　　　　　Score

I. Tree/False
(1) Linear Programming can be employed to solve problems with multiple objectives.线性规划可用来解决多目标的问题。
(2) In the search for an optimal solution, all points on the boundary of the feasible region must be considered.寻优过程中，可行域边界上所有的点都必须考虑。
(3) Changes in profit-contribution coefficients for basic variables will not affect the existing solution.基本变量的目标系数在允许范围内变化不影响当前解。
(4) Using opportunity costs is one way of handling an unbalanced transportation problem.
(5) A balanced transportation problem has the same number of supply points as demand points.
(6) The value of an additional unit of a resource, found in the last row under the artificial variables corresponding to the resource, is the shadow price for that resource.资源增加一个单位的价值是该资源的影子价格，可在最下一行对应人工变量的检验数处找到。
(7) The optimal value of the primal objective function is equal to the negative of the optimal value of the dual objective function.原问题的最优目标值等于其对偶问题的最优目标值的相反数。
(8) If a resource is not finished out, then its shadow price must be positive.若资源还没有耗尽，则此资源的影子价格是正的。
(9) The vertex of the feasible region of LP is: (multiple choices)线性规划可行域的顶点是：（可多选）
(A) feasible solution;可行解
(B) non-basic solution;非基本解
(C) basic feasible solution;基本可行解
(D) optimal solution;最优解
(E) basic solution.基本解
(A, B, C, D, E)
(10) If two LP problems are of the same optimal solutions, then 若两个线性规划问题的最优解相同，则
(A) the two LP problems are of the same constraints;这两个问题的约束条件相同
(B) the two LP problems are of the same objective functions;这两个问题的目标函数相同
(C) the two LP problems are of the same objective value;这两个问题的目标值相同
(D) all mentioned above are not correct.上述都不对
(A, B, C, D)

II. To solve the LP problems below:求解下面的线性规划

(1) Max. Z = 3X1 + 4X2 +X3
s.t. 2X1 + 3X2 +X3 ≤ 1
X1 + 2X2 +2X3 ≤ 3
X1, X2 , X3≥ 0
Please find out the optimal solution.找出最优解

(2) The objective function of an LP is Max. Z = 2X1 +4X2. This LP is of three constraints(resources #1,#2 and #3 respectively) with “≤”form. Below is a processing step by using simplex method.一问题的目标函数是Max. Z = 2X1 +4X2. 该问题的三个约束条件（资源#1,#2 和 #3）均是“≤”型。下方给出了单纯型法的一个步骤。

8/3
14/3
10/3
0
1
0
1
0
0
0
0
1
1/3
1/3
-1/3
-1/3
2/3
4/3

a) To complete this table;完成这张表
b) Is this table optimal? If “yes”, then do c); if “no”, then find out the optimal table.该表是否最优？若“是”，回答c)；若“否”，找出最优表
c) To write out the optimal solution and objective value.写出最优解和最优目标值
d) To write out the shadow prices of resources #1, #2 and #3, and describe the significanses.写出资源#1, #2 和#3,、的影子价格及其经济意义

III. To find the shortest path and its length from A to E:

B1 10 D1 5
13 2
C1 8
M 7 6
A 8 B2 D2 8 E
5 10 12
C2 5
13 8
B3 11 D3 4

Where M is the last two places of your ID number.

VI. To solve the transportation problem below:

D1
D2
D3
supply
S1
M+1
6
7
30
S2
4
3
5
45
S3
7
4
8
25
demand
60
30
10

Where M is the last place of your ID number.

IV. There is an LP problem below:有下面的线性规划问题
Max. Z = -5X1 + 5X2 +13X3
s.t. - X1 + X2 + X3 ≤20
12X1 +4X2 +10X3 ≤90
X1, X2 , X3≥ 0
a) Solve it;求解
b) Formulate its dual;写出其对偶问题
c) If resource #1 is changed to 18, what will Z be? What will the optimal solution be?若资源#1变成了 18，Z将如何？最优解如何？
d) If resources #1 and #2 are incressed by one unit respectively, what influences will be happened to Z?资源#1和#2分别增加一个单位，对Z有什么影响？
e) What is the allowed range for C3?求出C3的允许变化范围
f) What is the allowed range for b2? If b2 is decreased to 85, what is the optimal solution?求出b2的允许变化范围。若b2减少到85，最优解是什么？