GATE ME 2014 Set 2 — Question 28
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Question
If there are sources and destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is
Correct answer
(C) m + n - 1
Solution
In a transportation problem with origins (sources) and destinations, there are constraint equations (one for each row and column). However, since the total supply must equal total demand (), one of these equations is linearly dependent on the others. Therefore, there are independent equations. A basic feasible solution (BFS) is defined as a solution where the number of non-zero (basic) variables is equal to the number of independent constraints, which is .
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