Consider the following data for the transportation problem:

Since there is not enough supply, some of the demands at the three destinations may not be satisfied.
For the unsatisfied demands let the penalty costs be rupees 4, 5 and 6 for destinations (1), (2) and (3), respectively. Find the optimal allocation that minimises the transportation and penalty costs.

Factory Destination 1 2 3 Supply to be exhausted A 8 4 10 B 9 7 9 85 10 80 C 6 5 8 15 Demand 75 20 20 50