Question

Minimise $Z={\sum }_{j=1}^n{\sum }_{i=1}^m{c}_{ij}.x_{ij}$
Subject to ${\sum }_{i=1}^m{x}_{ij}=b_j,j=1,2,......n$
${\sum }_{j=1}^n{x}_{ij}=b_j,j=1,2,......,m$ is a LPP with number of constraints

• A. $m-n$
• B. $mn$
• C. $m+n$
• D. $\frac{m}{n}$

Answer 1

The correct option is C $m+n$

Constraints will be
$x_{11}+x_{21}+.....+x_{m1}=b_1$
$x_{12}+x_{22}+.....+x_{m2}=b_2$
$x_{1n}+x_{2n}+.....+x_{mn}=b_n$
$x_{11}+x_{12}+.....+x_{1n}=b_1$
$x_{21}+x_{22}+.....+x_{2n}=b_2$
$x_{m1}+x_{m2}+.....+x_{mn}=b_n$
So the total number of constraints $=m+n$