- The minimal spanning tree’s linear programming model is to minimize the sum of weights for branches in the tree, and the constraints utilize the 0-1 model and require ( ).
- If feasible domain for a linear programming problem has no boundaries, then the problem may ( ).
- The following statements about the Hungarian algorithm for assignment problem are correct. ( ).
- For what reason the product crowdfunding projects set the minimum sales requirement?（ ）。
- Some of the following statements are incorrect ( ).
- （）objective function （）constraints in the linear programming is/are（ ） of variables.
- There is an Euler circuit in the connected graph G, if and only if there is ( ) in G.
- “Please add a 0-1 variable to express the relationship between these two mutual exclusive constraints: x1≥0 or x1≤-20（ ）。
- Calculating test numbers is to ( ) unit freight of the odd-numbered cell and to ( ) unit freight of the even-numbered cell in the closed loop.。
- To apply the concept of expected value as a decision-making criterion with certain information, the decision maker should compute expected value by ( ) each decision outcome under each state of nature ( ) the probability of its occurrence.
- The process of Dijkstra Algorithm mainly focuses on labeling nodes with P and updating all nodes. The first step always starts with the first node v1, let P(v1) equal ( ) and label remaining nodes with the value of ( ).
- In the programming model of standard assignment problem(n assignees and n tasks), the number of decision variables is ( )
- The shadow prices of small blocks and big blocks are ( ) and ( ) respectively.
- In the transportation problem with supply volume greater than sales, in order to construct the balanced transportation sheet, we must （ ）。
- After we shorten the duration of 1→3 as this network shown, how does the indirect cost vary? ( )
- Given the conditional probabilities, Bayesian analysis can revise ( ) by ( ).
- The Hongmu Furniture Company produces tables. The fixed monthly cost of production is $6000 yuan, and the variable cost per table is $60 yuan. The retail price of a table is $180. Determine the monthly break-even volume for the Hongmu Furniture Company. （ ）
- The ESs of node 6 and node 7 are ( ) and ( ) respectively.
- What’s feasible solution? （ ）。
- When we solve the problem of maximization, the relationship between the optimal objective value of integer programming and that of its corresponding linear programming is ( ).
- What’s the value of the first choice that the company decides to explore it and surely find the oil? ( )
- In the Lego production problem, the optimal production plan(2 tables and 2 chairs) won’t change if the price of table varies within the range of ( ) and other conditions maintain unchanged.
- The earliest start time for an activity, called ES, is determined by the ( ) time that all preceding activities have been completed.
- The expected value and expected opportunity loss criteria result in the same decision. （ ）
- Both branch-and-cut technique and branch-and-bound technique are based on linear programming to solve integer programming. ( )
- There are three common techniques to solve integer programming, including branch-and-cut, branch-and-bound, and bionic algorithm.（ ）
- Kruskal Algorithm is called avoid cycle method, and it’s intuitive in the simple graph to get (n-1) pieces edges in the graph with n nodes. ( ）
- If the shadow price of a certain resource is p, then under other resources quantity unchanged, this kind of resource increases k units, the value of objective function must increase by pk.（ ）
- The optimal solution of integer programming is to find the corresponding linear programming optimal solution and then round it up. ( )
- During the process of calculating the lowest cost schedule, the shortest duration may afford a higher total cost in the project. ( )
- Transportation problems also belong to network flow problems particularly about allocation.（ ）
- When we solve a LP maximization problem by branch-and-bound, the objective function value of any feasible integer solution is the lower bound of this objective function value. ( ）
- The test numbers that are obtained by the closed loop method are not unique. ( ）
- Graph theory is to study the objects and their relationships, and it’s independent of the geometric shape of the graph. ( ）
- A conditional probability is the probability that an event will occur, given that another event has already occurred. ( )
- Dijkstra Algorithm can solve the shortest route problem of directed graph with positive weight or negative weight. ( )
- Under the expected value criterion, as long as the decision maker estimates the probability of occurrence of each state of nature, the expected value for each decision alternative can be computed. ( )
- The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized. ( )
- Decision tree consists of ( ).
- If the decision maker can gain the probability of each state by investigation, decision problem under uncertainty can be transformed to risky decision problem. ( ）
- The decision criteria, which include Maximax, Maximin, Minimax regret, Hurwicz, and Equal likelihood, will result in the same decision. ( )
- The method of decision-making problem includes ( ).
- In the Gantt charts, the horizontal axis represents time and the vertical axis represents each activity. （ ）
- When we carry on the calculation steps for the lowest cost schedule in networks, no matter how we shorten the duration of activities, the critical path won’t change. ( ）
- A virtual activity is used in an AOA network to show an actual passage of time, not just the precedence relationship. ( ）
- The critical activity in critical path is ( ).
- In terms of graph theory, the following statement is incorrect ( ).
- The Bellman algorithm can be used to find out the shortest route from v1 to any vertex, even the weight being negative. （ ）
- Dijkstra algorithm is only used to calculate the shortest route from the first vertex v1 to other vertices. ( ）
- The incorrect statement of transportation problem in the following statements is ( ).
- In the transportation model, the number of demand places and supply places is n and m respectively. The number of constraints is ( ).
- For the transportation problem of minimum value, the optimal transportation scheme can be gained when the test numbers are less than or equal to zero. ( ）
- When we adjust the transportation scheme by closed-loop method, the rule is that the maximum value of transportation increasing in the cell equals the minimum value of the numeral cell to be reduced, which is to ( ).
- Simply rounding off non-integer simplex solution values for models requiring integer solutions is not always appropriate. Rounding can often lead to suboptimal results. ( ）
- Branch-and-cut technique is only suitable for solving pure integer programming problems. ( ）
- A drilling team needs to determine 5 exploration wells from 10 alternative wells to minimize the total drilling cost. If 10 wells are represented by s1, s2, …s10, the costs being c1, c2, …c10, one of constraints is: if the plan chooses s3 or s4, then s5 cannot be selected and vice versa. We set a 0-1 variable, xj(j=1, 2, …10), then this constraint can be expressed ( )
- Assignment problem doesn’t belong to 0-1 integer programming problem. ( ）
- Shadow price is actually a marginal price. ( ）
- The following statements of 100% rule of objective function coefficient is correct（ ）.
- The duality of a dual problem is not necessarily the primal problem. ( ）
- If the primal problem of linear programming adds a constraint, it is equivalent to adding a variable to the dual problem.（ ）
- The following features of standard form of Linear programming are correct（ ）.
- The optimal solution of the linear programming problem must be the feasible solution. （ ）
- If the optimal solution of the linear programming problem is reached at two vertices of feasible domain at the same time, then the optimal solution has ( ).
- If the graphical method is used to solve the linear programming problem, the number of decision variables should be ( ).
- In the linear programming model, ( ) restrict the decision variables to zero or positive values.
- Manufacturing companies develop linear programming models to help decide how many units of different products they should produce to maximize their profit (or minimize their cost), given scarce resources such as capital, labor, and facilities. ( ）
- In general, an increase in variable costs will（ ）the break-even point, all other things held constant.
- It’s important to make full use of techniques in management science process, which techniques are commonly used for the purpose of decision-making（ ）?
- The purpose of break-even analysis is to determine the number of units of a product to sell or produce that will equate total revenue with total cost. At the break-even point, the profit is ( ) zero.
答案:Only one edge entering each node except for the root###At least one edge connecting the root with other nodes
答案:No infinite optimal solution###Infinite optimal solutions###Unique optimal solution###Finite optimal solution
答案:The first step of Hungarian Algorithm needs to guarantee at least one 0 element in each row and column###What we ought to do is cover all 0 elements with the fewest straight lines###When we perform a trial assignment, we repeat crossing out those extra 0 elements until the number of 0 elements selected equal to the order of new matrix
答案:Manufacturing cost structure###Operating factors###Economies of scale
答案:Basic solution is a solution greater than 0###The optimal solution to LP is unique
答案:Both and linear functions
答案:no odd vertex
答案:-My≤x1,x1+20≤M(1-y),y=0 or 1,M is a sufficiently large positive number
答案:add; subtract
答案:multiplying; by
答案:0; ∞
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