Question

Minimise \( Z=\sum_{i=1}^{n}\sum_{j=1}^{m} c_{ij}x_{ij} \) subject to \[ \sum_{i=1}^{m} x_{ij}=b_j,\; j=1,2,\ldots,n, \] \[ \sum_{j=1}^{n} x_{ij}=b_i,\; i=1,2,\ldots,m. \] This is an LPP with number of constraints equal to

• A. \(m-n\)
• B. \(mn\)
• C. \(m+n\)
• D. \(\dfrac{m}{n}\)

Hint:

Transportation problems have \(m+n\) constraints.

Answer 1

The Correct Option is C

Step 1: There are \(n\) constraints from column sums.
Step 2: There are \(m\) constraints from row sums.
Step 3: Total constraints \(=m+n\).