Question 3 (i) Transportation and location-allocation problems are widely studied and applied in real- world situations. They are similar in nature. Identify three commonalities and five differences of these two optimisation problems. (8 marks) (ii) The logistics distribution network for an Australian based electric vehicle manufacturing company consists of three suppliers, two manufacturers, three warehouses, and two retailers. Supplier capacities and shipping costs per unit (in dollars) from each supplier to each manufacturer are as follows: Manufacturer Supplier Japan South Korea Capacity China 36 32 45,000 India 48 44 33,000 Thailand 58 56 22,000 The shipping costs per unit (in dollars) from each manufacturer to each warehouse are: Warehouse Manufacturer Japan Singapore Malaysia Indonesia 66 64 62 South Korea 58 56 54 Customer demand and shipping costs per unit (in dollars) from each warehouse to each retailer are: Retailer Warehouse Melbourne Doncaster Singapore 26 28 Malaysia 24 26 Indonesia 22 24 Demand 56,000 44,000 Shipping costs per unit (in dollars) from each retailer to another are: Retailer Retailer Melbourne Doncaster Melbourne Doncaster 6 6 Construct a transportation table for the above four-echelon transshipment problem. Then, formulate the LP model for the problem using the approach discussed in this subject. (Hints: use S1, S2, and S3 to denote the suppliers, use M4 and M5 to denote the manufacturers, use W6, W7, and W8 to represent warehouses, and use R9 and R10 to represent the retailers.) (12 marks) (iii) A start-up real estate agent has four property consultants and five new branches across Melbourne. It wants to assign the consultants to the branches to maximise profit ($100,000). The profit generated by each consultant in each branch is shown in the following table: Branch Consultant A B C D E 1 $7 $20 $14 $8 $10 2 $14 $13 $20 $9 $11 3 $3 $6 $9 $7 $10 4 $11 $7 $16 $9 $10 Because of personal preference, consultant 3 must not be assigned to branch A, and consultant 4 cannot be assigned to branch E. Formulate a balanced assignment model to the above optimisation problem. (5 marks)