R Sukraj Assignment 1- Transportation and Assignment models Question 1 Total Marks=50 PND Manufacturers is a water-bottling company with plants in Durban, Johannesburg, and Cape Town. In order to reach their customers around the country, they have set up warehouses in Mangaung,Mbombela, and Gqeberha. The logistics manager wants to find the distribution model, from plant to warehouse, that will bring about the lowest cost. The manager has the following information available: Warehouse Requirements: Mangaung needs to receive 100 cases of bottled water per month, Mbombela needs 450, and Gqeberha needs 275. Plant output: Durban can produce 300 cases each month, Johannesburg produces 375, and Cape Town produces 150. The shipping cost per case from: Durban to Mangaung is R 20 Durban to Mbombela is R 18, Durban to Gqeberha is R 10. Johannesburg to Mangaung is R 25, Johannesburg to Mbombela is R 15, and Johannesburg to Gqeberha is R9. Cape Town to Mangaung is R13, Cape Town to Mbombela is R15, and Cape Town to Gqeberha is R24. 1.1 Use the Northwest corner rule to calculate the initial solution for the number of cases that should be shipped from each plant to each warehouse at the minimum cost. (10) 1.2 Use the Stepping-Stone method to improve the initial solution. Show all closed paths, calculations for improvement indexes and the costs for the final solution 1.3 Use MS Excel Solver to determine the optimum solution. (25) (15)