Consider the following transportation problem:

(a) Find optimal solution to this problem and determine the total cost of transportation.

(b) Is the optimal solution unique? If there is an alternate optimal solution, identify it.

(c) If the transporter agrees to reduce the transportation charges on the route B-S by 40 per cent, how will it affect the optimal solution?

(d) It is decided to send a total of 150 units on the route A-P. How will the optimal solution and total cost be affected?

(e) Trace the effect of sending 100 units on the route C-S.

(f) Within what limits a change in the cost element of the route C-P will have no effect on the current optimal solution?

Destination Source P Q R S Supply ABCD 6 11 9 8 200 13 10 8 15 300 9 9 14 12 500 12 10 12 10 100 Demand 350 250 300 200