1、1XXXX 学年第 X 学期运筹学期末试卷Class ID Number Name ScoreI. True/False(1) A balanced transportation problem has the same number of supply points as demand points.(2) In the search for an optimal solution of an LP problem, only vertexes of feasible region are needed to be considered.(3) The stepping stone meth
2、od is used because the transportation problem cannot be solved via the simplex method.(4) Linear Programming can be employed to solve problems with single objective. (5) If a resource is not finished out, then its shadow price must be positive.(6) The first step in applying the simplex method is to
3、transform all inequality constraints into equality constraints by adding slack variables and subtracting surplus variables.(7) The optimal value of the primal objective function is equal to the optimal value of the dual objective function.(8) If a constraint is in “” form in LP problem, then artific
4、ial variable is necessary.(9) That the feasible region of LP is not empty means: (A) it includes the origin X=(0,0,0);(B) it is bounded;(C) it is unbounded;(D) it is convex.(A, B, C, D)(10) Both the primal and dual problems are of feasible solution, then may be(A) an optimal solution is available fo
5、r primal problem, but the optimal solution is not available for dual problem;(B) at least one problem is unbounded;(C) an optimal solution is available for one problem, and the other problem is of unbounded solution;(D) both the primal and dual problems might be of optimal solution.(A, B, C, D)2II.
6、To solve the problems below:(1) Min. w = 14X1 + 20X2 s.t. X1 + 4X2 4X1 + 5X2 22X1 + 3X2 7X1, X2 0Please find out the optimal solutions for both this problem and its dual.(2) The objective function of an LP is Max. Z = 5X1 +6X2 +8X3. This LP is of two constraints (resources #1 and # 2 respectively) w
7、ith “”form. Below is a processing step by using simplex method.2551/2-1/23/2-1/2101/2-3/201a) To complete this table;b) Is this table optimal? If “yes”, then do c); if “no”, then find out the optimal table.c) To write out the optimal solution and objective value.d) To write out the shadow prices of
8、resources #1 and #2, and describe the significances.3III. To find the shortest path and its length from A to E:7B1 C1 1 6 4 4 D1M+12 3 6A 4 B2 2 C2 E3 4 344 1 3 D2B3 3 C3 3 M is the last place of your ID number.VI. To solve the transportation problem below:D1 D2 D3 supplyS1 M+1 1 8 12S2 2 4 1 14S3 3
9、 6 7 4demand 9 10 11M is the last place of your ID number.4IV. A factory is going to produce Products I, II and III by using raw materials A, B and C. The related data is shown below:Raw material I II III Raw material availableABC2 1 11 2 32 2 1200 (kg)500 (kg)600 (kg)Profit ($) 4 1 3a) Please arran
10、ge production plan to make the profit maximization.b) If one more kg of raw material A is available, how much the total profit will be increased?c) The market price for raw material B is $1.2. Will the factory buy it or sell it? Why?d) What is the allowed range for raw materials A, B and C respectively?e) What is the allowed range for the profit of product II?
