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# Part 3 MEI mathematics test 18 targets 5 questions

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**10.01.2014**

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# Description

Task 1

Question 1. Let A and B - set. What is the record?

1. Set A is a proper subset of the set, which is a true subset of the set-set A

2. Sets A and B are endless

3. The sets A and B are finite

4. The sets A and B are not empty

5. The sets A and B are equal

Question 2. Let A be a non - empty set of all students at the school, in - a lot of fifth grade students of this school, C - the set of seventh grade students of this school. Which records expresses a false statement? (Parentheses here, as in arithmetic expressions, set procedures).

1.

2.

3.

4.

5.

Question 3. Which of the following statements is not always (not for any sets A, B, C) is true?

1.

2.

3.

4.

5.

Question 4. Let - a lot of days of the week, as well - a lot of days in January. What is the cardinality of the set?

1. 38

2. 217

3. 365

4. 31

5. 7

Question 5: Consider the set of the clock that can be asserted with respect to the element and the sets? .

1.

2.

3.

4.

5.

Task 2

Question 1. Consider the G line between A and B. In a case called line-specific INDICATES everywhere?

1.

2.

3.

4.

5.

Question 2. Assume that there exists a one-to-one correspondence between the sets G and B. What can be said about their powers?

1.

2.

3.

4.

5.

...

Task 18

Question 1. What is the statement of the problem in terms of the general problem of dynamic programming:

1. Find the maximum of the function under conditions

2. Find the minimum of the function under conditions

3. Find the minimum of the function under conditions

4. Select a control strategy to ensure maximum function

5. Find the maximum of

Question 2: What kind of problems are the problems of the form under the conditions

1. Linear programming

2. The problem of dynamic programming

3. The problem of nonlinear programming

4. The transportation problem

5. The integer linear programming problem

Question 3. Specify an expression representing the main functional Bellman equation or recurrence:

1.

2.

3.

4.

5.

Question 4. How do I get the optimal control strategy using dynamic programming?

1. In one step

2. n stages; first, the optimal strategy is sought on the 1st step and then at the 2nd, etc. up to the last n-th step,

3. n stages; first, the optimal strategy is sought on the 1st step, then the first two steps, then the first three steps, etc., including the last n-th step.

4. In the n stages; first optimal strategy is sought on the n-th step, then (n-1) th, then (n-2) -th, etc. up to the 1st step.

5. n stages; first, the optimal strategy is looked at the n-th step, then the last 2 steps, then on a 3-on-Latter etc. up to the first step.

Question 5. What is the wording of the formulation in terms of dynamic programming for a backside-chi:

The structure of the production association consists of two companies, which are interconnected in a cooperative rates. By investing additional funds for the development of these enterprises, it is possible to improve technical and economic performance of the production association as a whole, thus ensuring to obtain additional profit. The magnitude of this profit depends on how much funds are allocated to each enterprise-yatiyu and how those funds are used. Considering that the development of i-venture at the beginning of the k-th year is allocated thousand. Rub., To find a version of the distribution of funds between enterprises during N years, which will provide Vaeth receive in a given period of maximum profit.

1. The criterion under the conditions

2 - The state of the system at the beginning of the k-th year - management;

Criterion

3 - The state of the system at the beginning of the k-th year - Management

4. The criterion under the conditions

5. - Management

Criterion

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