Question

Minimise $Z=\displaystyle\sum_{j=1}^{n} \displaystyle\sum_{i=1}^{m} c_{i j} \cdot x_{i j}$ Subject to $\displaystyle\sum_{ i =1}^{ m } x _{ ij }= b _{ j }, j =1,2, \ldots \ldots n$ $\displaystyle\sum_{j=1}^{n} x_{i j}=b_{j}, j=1,2, \ldots \ldots, m$ 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

Constraints will be
$x_{11}+x_{21}+...+x_{m 1}=b_{1}$
$x_{12}+x_{22}+...+x_{m 2}=b_{2}$
$x_{1 n}+x_{2 n}+...+x_{m n}=b_{n}$
$x_{11}+x_{12}+...+x_{\ln }=b_{1}$
$x_{21}+x_{22}+...+x_{2 n}=b_{2}$
$x_{m 1}+x_{m 2}+...+x_{m n}=b_{n}$
So the total number of constraints $= m + n$