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For the standard transportation linear program with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destination j) is desired. The best upper bound for this number is
[2008]
 
  • a)
    m n
  • b)
    2(m + n)
  • c)
    m + n .
  • d)
    m + n – 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
For the standard transportation linear program with m sources and n de...
In such an L .P.P, m × n variables are th ere an d m + n equations/constraints are there (satisfying the demand-supply requirements). But one constraint is removed as total supply equals total demand.  The best upper bound xij values is (m + n  1).
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For the standard transportation linear program with m sources and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destination j) is desired. The best upper bound for this number is[2008]a)m nb)2(m + n)c)m + n .d)m + n – 1Correct answer is option 'C'. Can you explain this answer?
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