Linear Programming Question 113
Question: Minimize $ z=\sum\limits _{j=1}^{n}{{}}\sum\limits _{i=1}^{m}{c _{ij}x _{ij}} $ Subject to : $ \sum\limits _{j=1}^{n}{x _{ij}\le a _{i},\ i=1,…….,m} $ $ \sum\limits _{i=1}^{m}{x _{ij}=b _{j},\ j=1,……,n} $ is a (L.P.P.) with number of constraints
[MP PET 1999]
Options:
A) $ m+n $
B) $ m-n $
C) mn
D) $ \frac{m}{n} $
Show Answer
Answer:
Correct Answer: A
Solution:
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}\to $ 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}\to n $
constraints
Total constraints = $ m+n $ .
BETA
