The stable distribution for the matrix 1 2 3 4 1 2 3 4 [ 0.20 0.10 0.05 0.05 0.30 0.20 0.20 0.30 0.40 0.40 0.50 0.40 0.10 0.30 0.25 0.25 ] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

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Answer 1

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Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

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7. [10 marks] Let G = (V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a cycle in G on which x, y, and z all lie. (a) First prove that there are two internally disjoint xy-paths Po and P₁. (b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that there are three paths Qo, Q1, and Q2 such that: ⚫each Qi starts at z; • each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are distinct; the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex 2) and are disjoint from the paths Po and P₁ (except at the end vertices wo, W1, and w₂). (c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and z all lie. (To do this, notice that two of the w; must be on the same Pj.)

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4. [10 marks] Find both a matching of maximum size and a vertex cover of minimum size in the following bipartite graph. Prove that your answer is correct. ย ພ

Answer 2

Question

Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

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Answer 3

Question

Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

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Answer 4

Question

Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

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Answer 5

Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

Answer 6

Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

Answer 7

Chapter 8, Problem 17RE

(a)

To determine

To calculate: The stable distribution for the matrix 1 2 3 41234[0.200.100.050.050.300.200.200.300.400.400.500.400.100.300.250.25] and also interpret for the situation that a reservoir holds up to 4 units of water and the policy for the use of water for the irrigation and drinking purpose is that it never allows the content of reservoir to drop below 1 unit of water.

Answer 8

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

Answer 9

(b)

To determine

To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

Solution Summary: The author calculates the stable distribution for the provided matrix left[c1221683,

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To calculate: The average weekly benefits to be realized in the long run if the weekly benefits to recreation in the area around reservoir is estimated to be $4000,$6000,$10,000 and $3000 for the 1, 2, 3 and 4 units respectively in the reservoir.

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