Is there a structure to the solution of the following linear program?

$\min_{x_{ij} } \sum_{i,j} x_{ij} \mu_{ij}$

$s.t. \forall j, \sum_{i} x_{ij} = \beta_j,$ row sum

$\forall i, \sum_{j} x_{ij} D_{ij} \leq 1,$ column sum


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