Question 1 Consider the following distribution problem from 4 plants to 4 customers for the HighQuality Chemicals Company Limited.

(a) Apply the least-cost-first rule to determine a starting solution. Then, find the minimum shipping schedule and the corresponding total cost. (25 marks)

(b) Suppose that there is an increase in the unit shipping cost from P3 to C3 by $y. What is the smallest value of y that the minimum shipping schedule obtained in (a) starts to change? Find also an alternative minimum shipping schedule and the corresponding total cost in this case.

Unit shipping costs to customers ($) C2 C4 Plants P1 4 Capacity 200 250 P2 1 Sampo 14 P3 11 9 350 12 200 P4 Demand 7 200 100 300 400