A company producing aluminum is supplied with bauxite from four mines (01,02,03, and 04 ) which produce 3,7,5, and 9 thousand tones of mineral per week respectively. There are 4 modes of transportation of bauxite to the factory: by ship (T1) - by trucks (T2) - by a simple railway wagon (T3) - by special railway wagons (T4). The total capacity per day is 4 thousand tones for ships, 3 thousand for cars and 4 thousands each one of the two types of rail. Transportation costs per tone are given in the following table. (a) Design the problem as a transportation model. (b) Use the northwest corner method for finding the initial basic possible solution to the problem. c) Use Vogel's method for finding the initial feasible solution of the problem. d) Starting with the initial basic feasible solution of the question (b) or (c), use the modified distribution (modi) method to find the optimal solution