Minimize $z=\sum\limits_{j=1}^n \sum\limits_{i=1}^m c_{i j} x_{i j}$

Subject to : $\sum\limits_{j=1}^n x_{i j} \leq a_i, i=1 ..., m ; \sum\limits_{i=1}^m x_{i j}=b_j, j=1 ..., n$ is a LPP with number of constraints

$m+n$

(I) Condition, $i=1, x_{11}+x_{12}+x_{13}+..........+x_{1 n} \leq a_1$

$i=2, x_{21}+x_{22}+x_{23}+..........+x_{2 n} \leq a_2$

$i=3, x_{31}+x_{32}+x_{33}+..........+x_{3 n} \leq a_3$

......................

$i=m, x_{m 1}+x_{m 2}+x_{m 3}+..........+x_{m n} \leq a_m \rightarrow$ m constraint s

(II) Condition $j=1, x_{11}+x_{21}+x_{31}+..........+x_{m 1}=b_1$

$j=2, x_{12}+x_{22}+x_{32}+..........+x_{m 2}=b_2$

......................

$j=n, x_{1 n}+x_{2 n}+x_{3 n}+..........+x_{m n}=b_n \rightarrow$ n constraints

∴  Total constraints = m + n.