b) Table 2 shows the transportation costs, demands and supplies of a transportation problem. Table 2: Transportation problem To From A В Supply 1 6 7 4 150 8 11 50 10 11 12 250 Demand 100 200 150 i) Find the initial solution using the Minimum Cost method and identify the special case if any. ii) Suppose the initial solution to the above problem takes the basic variables X11 = 100, x12 = 50, x23 = 50, x32 = 150 and x33 = 100. Find the optimal solution using Modified Distribution method. iii) Present the optimal solution obtained in ii) graphically.

Q4. Solve the following transportation problem using the following table. Obtain an Initial BFS to the following Transportation problem using NORTH WEST CORNER RULE method? D1 D2 D3 D4 SUPPLY 01 1 7 4 300 02 2 400 03 8 3 3 2 500 DEMAND 250 350 400 200 1200 5

4. Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively.  Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Set up the solution in Excel and solve with Solver. What are total costs?

Develop a LP model for the transportation problem (cost problem). Solve the LP model   to find the optimal solution and the minimum total cost.