Question

Minimize $z = \sum^{n}_{j =1}\sum ^{n}_{i =1} c_{ij} x _{ij} $
Subject to : $\sum ^{n}_{j =1}x_{ij} \le a_{i } , i = 1,.........,m$
$\, \, \, \, \, \, \, \, \, \, \sum ^{n}_{i=1} x_{ij} = b_{j} , j = 1,.......,n$
is a (L.P.P.) with number of constraints

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

Answer 1

Answer: (A)

Condition (i),
$i = 1, x_{11 } +x_{12} +x_{13} +.....+ x_{1n}$
$ i = 2, x_{21} +x_{22} +x_{23} + .... + x_{2n}$
$ i=3, x_{31} + x_{32} +x_{33} +.....+x_{3n}...............$
$ i = m, x_{m1} +x_{m2} + x_{m3} + ..... x_{mn } \rightarrow$ constraints
Condition (ii),
$ j = 1, x_{11}+x_{21}+x_{31} + .......+x_{m1}$
$ j =2, x_{12} + x_{22} +x_{32} + .....+x_{m1}............$
$ j=n, x_{1n} + x_{2n} +x_{3n} + .... +x_{mn} \rightarrow n$ constraints
$ \therefore $ Total constraints = $= m + n $