# Linear Programming with constrained sum of rows and sum of columns

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