Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 2, Problem 12RP
Explanation of Solution
Relating two
Suppose that
Since 10% of the rural residents moved to city, remaining 90% of the rural decided to continue to stay at the rural residents at the beginning of the year t+1.
Thus, the number of rural residents in the beginning of the year t+1 is given below:
Also, 20% of city residents moved to the rural residents in the beginning of the year t+1.
Therefore, the number of city residents in the beginning of the year t+1 is as follows:
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Let y be a column vector: y = [1, 2, 3, 4, 5, 6] so that y.shape = (6,1). Reshape the vector into a matrix z using the numpy.array.reshape and (numpy.array.transpose if necessary) to form a new matrix z whose first column is [1, 2, 3], and whose second column is [4, 5, 6]. Print out the resulting array z.
Problem 1) Change the diagonal elements of a 3X3 matrix to 1.
Diagonal elements of the example matrix shown here are 10, 8, 2
10 -4 0
7 8 3
0 0 2
Read the given values from input (cin) using for loops and then write your code to solve the diagonal.
Consider the following problem.
INPUT: Positive integers r1, ··· , rn and c1, ··· , cn .
OUTPUT: An n by n matrix A with 0/1 entries such that for all i the sum of the ith row
in A is ri and the sum of the ith column in A is ci , if such a matrix exists.
Think of the problem this way. You want to put pawns on an n by n chessboard so that the
ith row has ri pawns and the ith column has ci pawns.
Consider the following greedy algorithm that constructs A row by row. Assume that the
first i-1 rows have been constructed. Let aj be the number of 10
s in the jth column in the
first i-1 rows. Now the ri columns with with maximum cj -aj are assigned 1’s in row i, and
the rest of the columns are assigned 00
s. That is, the columns that still needs the most 1’s
are given 1’s. Formally prove that this algorithm is correct using an exchange argument.
Chapter 2 Solutions
Operations Research : Applications and Algorithms
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.2 - Prob. 1PCh. 2.3 - Prob. 1PCh. 2.3 - Prob. 2P
Ch. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Prob. 9PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2 - Prob. 1RPCh. 2 - Prob. 2RPCh. 2 - Prob. 3RPCh. 2 - Prob. 4RPCh. 2 - Prob. 5RPCh. 2 - Prob. 6RPCh. 2 - Prob. 7RPCh. 2 - Prob. 8RPCh. 2 - Prob. 9RPCh. 2 - Prob. 10RPCh. 2 - Prob. 11RPCh. 2 - Prob. 12RPCh. 2 - Prob. 13RPCh. 2 - Prob. 14RPCh. 2 - Prob. 15RPCh. 2 - Prob. 16RPCh. 2 - Prob. 17RPCh. 2 - Prob. 18RPCh. 2 - Prob. 19RPCh. 2 - Prob. 20RPCh. 2 - Prob. 21RPCh. 2 - Prob. 22RP
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