Question

A cement company has three factories which transport cement to four distribution centres. The daily production of each factory, the demand at each distribution centre, and the associated transportation cost per tonne from factory to distribution centre are given in the Table. 

Hint:

The Least Cost Method involves selecting the lowest cost cell in the transportation matrix and allocating as much as possible. Repeat until all supplies and demands are met.

Answer 1

Correct Answer: 112000

The transportation problem can be solved using the Least Cost Method. The least cost in the matrix is selected, and we allocate the maximum possible supply to that cell. We continue this process until all demands and supplies are fulfilled. Initial Matrix: \[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Factory} & D_1 & D_2 & D_3 & D_4 & \text{Supply}
\hline F_1 & 20 & 30 & 110 & 70 & 600
F_2 & 10 & 0 & 60 & 10 & 100
F_3 & 50 & 80 & 150 & 90 & 1000
\hline \text{Demand} & 700 & 500 & 300 & 200 &
\hline \end{array} \] By following the Least Cost Rule, we find the initial basic feasible solution: - Assign 100 tonnes from F1 to D2 (cost: 30)
- Assign 500 tonnes from F3 to D2 (cost: 80)
- Assign 100 tonnes from F2 to D4 (cost: 10)
- Assign 200 tonnes from F1 to D1 (cost: 20)
Thus, the initial basic feasible solution (in integer) is: \[ \boxed{112000} \]