This qurstion is about linear programming and please answer the question in the image.

A mining company extracts gravel, the basic product it sells, from four mines, M1, M2, M3 and M4. The weekly production of each mine is 25, 30, 20 and 30 tons of gravel respectively. The gravel has to be transported to four main consumers, C1, C2, C3, C4 and C5 requiring for their needs 20, 20, 30, 10 and 30 tons of gravel per week respectively. The transportation cost in hundred dollars per ton of gravel in the following table. C1 C2 C3 C4 C5 M1 10 2 3 15 9 M2 5 10 15 2 4 M3 15 5 14 7 15 M4 20 15 13 6 8 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) Set up the initial tableau by the minimum cost method and find the minimization of the total shipping cost. b) Suppose that the shipping link between M1 and C3 is unavailable temporarily. Set up the initial tableau by Vogels method to minimize the total shipping cost of meeting each mills demand.

10 15 9 A mining company extracts gravel, the basic product it sells, from four mines, M1, M2, M3 and M4. The weekly production of each mine is 25, 30, 20 and 30 tons of gravel respectively. The gravel has to be transported to four main consumers, C1, C2, C3, C4 and C5 requiring for their needs 20, 20, 30, 10 and 30 tons of gravel per week respectively. The transportation cost in hundred dollars per ton of gravel in the following table. C3 C4 Cs. M M25 10 15 2 4 M315 5 14 7 15 M4 20 15 13 6 8 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) Set up the initial tableau by the minimum cost method and find the minimization of the total shipping cost. b) Suppose that the shipping link between Mj and C3 is unavailable temporarily. Set up the initial tableau by Vogel's method to minimize the total shipping cost of meeting each mill's demand