IE Electronic has three plants in California, Arizona, and Texas and two major distribution centers in Nevada, Florida and North Dakota. The capacities of each plant are 1000 products, and the demands at the two distribution centers for the same period are 2300 and 1400 products. Because of the deregulation of airfares, Company believes that it may be better to first fly some products to Nebraska or Montana and then fly them to their final destinations. The mileage chart between the plants and the distribution centers is given in Table. The company in charge of transporting the products charges $0.08 per mule. There is a penalty for each unmet distribution center demand as $0.05 per mile Minimize the shipping cost Nevada Florida North Dakota Nebraska Montana California 1250 1000 1350 2690 2690 Arizona 1000 1275 1250 1250 1275 Texas 1350 1350 1000 1350 1000 Nebraska 1275 2690 1275 1350 Montana 2690 1250 2690 1000 these questions according to problem given above Set up mathematical model Draw the network. Convert to transportation table from network Solve this problem by using vogel's method Check the optimality by using transportation simplex and explain why it is optimal or not? If it is not optimal, reach the optimal solution (Hint Firstly you must know initial solution) Suppose that we change the coefficient of Xaj (select basic variable arbitrarily). If we want to protect cur optimal value, show the allowable increase and decrease for delta as an interval (Hint Firstly you must reach optimal solution)