1. (35 marks) TireXR has plants at Node 1 and Node 2 producing tires at weekly rates of 2500 units and 3500 units respectively. The units are transported to one of the two warehouses at Node 3 and Node 4, and then to retailers at Node 6, Node 7 and Node 8. The transport costs per unit (in dollars) and demands of the retailers are shown below. Node 3 5 4.2 4.5 5.5 4 1 2 Node 1250 = 1500 5 demand 9.2 7.2 6 demand 8.5 8 7 demand = 2000 6.2 5.2 3 4 The objective is to find the cheapest transport scheme. Let Xij be the number of units to be transported from Node i to Node j. Solve the LP problem using Excel and answer the following questions on Moodle. Question 1.1: Fill in the boxes in the partial Excel spreadsheet (provided in Moodle). Question 1.2: Find the optimal transport scheme. Question 1.3: Find the minimum total transport cost. Question 1.4: If the unit transport cost from Node 4 to Node 6 is to decrease, what is the lowest cost it can decrease to without changing the optimal transport scheme? Question 1.5: If the unit transport costs from the Node 1 to the warehouses are all decreased by 1.5 dollars, what is the total percentage change? Find the minimum total cost. Question 1.6: If the demands of the three retailers are each decreased by 150 units, what is the total percentage change? Find the change in minimum total cost. 1. (35 marks) TireXR has plants at Node 1 and Node 2 producing tires at weekly rates of 2500 units and 3500 units respectively. The units are transported to one of the two warehouses at Node 3 and Node 4, and then to retailers at Node 6, Node 7 and Node 8. The transport costs per unit (in dollars) and demands of the retailers are shown below. Node 3 5 4.2 4.5 5.5 4 1 2 Node 1250 = 1500 5 demand 9.2 7.2 6 demand 8.5 8 7 demand = 2000 6.2 5.2 3 4 The objective is to find the cheapest transport scheme. Let Xij be the number of units to be transported from Node i to Node j. Solve the LP problem using Excel and answer the following questions on Moodle. Question 1.1: Fill in the boxes in the partial Excel spreadsheet (provided in Moodle). Question 1.2: Find the optimal transport scheme. Question 1.3: Find the minimum total transport cost. Question 1.4: If the unit transport cost from Node 4 to Node 6 is to decrease, what is the lowest cost it can decrease to without changing the optimal transport scheme? Question 1.5: If the unit transport costs from the Node 1 to the warehouses are all decreased by 1.5 dollars, what is the total percentage change? Find the minimum total cost. Question 1.6: If the demands of the three retailers are each decreased by 150 units, what is the total percentage change? Find the change in minimum total cost
