Minimize z = ∑nj =1∑ ni =1 cij x ij Subject to: ∑ nj =1xij le ai , i = 1,.........,m ∑ ni=1 xij = bj , j = 1,.......,n is a (L.P.P.) with number of constraints

Question

Minimize z = ∑nj =1∑ ni =1 cij x ij Subject to: ∑ nj =1xij le ai , i = 1,.........,m ∑ ni=1 xij = bj , j = 1,.......,n is a (L.P.P.) with number of constraints (A) m + n  (B) m - n  (C) m n  (D) (m/n)

Tardigrade Admin · Accepted Answer

Condition (i), i = 1, x11 +x12 +x13 +.....+ x1n i = 2, x21 +x22 +x23 + .... + x2n i=3, x31 + x32 +x33 +.....+x3n............... i = m, xm1 +xm2 + xm3 + ..... xmn arrow constraints Condition (ii), j = 1, x11+x21+x31 + .......+xm1 j =2, x12 + x22 +x32 + .....+xm1............ j=n, x1n + x2n +x3n + .... +xmn arrow n constraints ∴ Total constraints = = m + n

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

$m + n$

$m - n$

$mn$

$\frac{m}{n}$

Q. Minimize z=∑j=1n​∑i=1n​cij​xij​ Subject to : ∑j=1n​xij​≤ai​,i=1,.........,m ∑i=1n​xij​=bj​,j=1,.......,n is a (L.P.P.) with number of constraints

m+n

m−n

mn

nm​

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

$m + n$

$m - n$

$mn$

$\frac{m}{n}$