6. [24 points] A mining company extracts gravel, the basic product it sells, from four mines, M, M2, M3 and M4. The weekly production of each mine is 25, 30, 35 and 20 tons of gravel respectively. The gravel has to be transported to five main consumers, C1, C2, C3, C4 and C5 requiring for their needs 20, 15, 35, 10 and 30 tons of gravel per week respectively. The transportation cost in hundred dollars per ton of gravel in the following table. C C2 C3 C4 C5 M 7 6 10 15 9 M2 10 8 20 17 15 M3 11 5 14 8 11 M4 20 9 The problem is to devise a shipping schedule that will meet the demand at each consumer with the supply available at each mine and minimize the total shipping cost. a) (5 points) Set up the initial tableau by the minimum cost method, the least cost method, Northwest corner method and Vogel's method separately. b) (8 points) Find the minimization of the total shipping cost. c) (11 points) Suppose that the shipping link between M3 and C4 is unavailable temporarily. Set up the initial tableau by Vogel's method to minimize the total shipping cost of meeting each mill's demand. 13 10 18