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A shop has 4 workers and 4 works to be performed The estimate of time...

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Algebra

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A shop has 4 workers and 4 works to be performed The estimate of time man hours each man will take to perform each project is given in the following table How should the works to be allotted so as to optimise the total work 1 2 3 4 1 2 3 1 4 19 2 3 4 Solution Step 1 Given matrix is 1 1 8 2 13 3 4 38 19 8 13 38 19 26 0 9 23 28 4 26 9 26 24 10 Step 2 Here the given matrix is a square matrix Hence the assignment problem is a balanced problem Subtracting minimum cost of each row of the cost matrix we obtain the following matrix 17 2 3 4 11 26 17 11 18 15 28 4 26 1 2 3 4 19 18 15 26 24 10 18 24 4 16 9 3 0 22 3 0 28 14 0 Step 3 Subtracting minimum cost of each column of the modified cost matrix we obtain the following matrix 12 3 4

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