4. Transportation problem (TP). 1 J K 3 2 L_Supply 8 11 5 3 2 1 B 14 5 2 6 3 C 11 Demand 12 7 8 9 Table 1: Detailed data of this minimization TP a. Define variables and find the linear programming formulation of the trans- portation problem minimize the total cost) as given in transportation table (Table 1)? 2 marks b. Find the initial solution and the corresponding cost by the North-West Corner rule. 3 marks 3. (Duality, Complementary slackness). Consider the following simple linear pro- gram: (min)f(x) = -2.6, -12 st. *1 + x2 0. (a) Write the dual of this linear program. 4 marks (b) By inspection, determine all basic feasible solutions to the dual. Which of these solutions are optimal? (Be sure your stated solutions are solutions to the dual of the LP in the form given. Changing the LP to an equiv- alent form may change the sign of the dual solution.) EXPLAIN YOUR METHOD. 7 marks