Q4. (a) Suppose the initial basic feasible solutions for the following (3 x 3) transportation model with the given supply, demand and transportation cost per unit (RM) are given as follows: Supply (i,j) S1 12 Sources Destinations D D2 D 9 10 4 10 2 7 6 12 3 5 10 3 10 10 5 15 S2 8 10 S3 Demand Find the reduced cost for all the non-basic variables by assuming the reduced cost is derived using 7=C-u, -v;, where c, is the cost per unit of flow from source i to destination, while u, and v; (i=1, 2, 3;j =1, 2, 3) are the simplex multiplier (5 marks) (11) Based on the answer in part (1), discuss the effects of reduced cost on the objective function's value if a non-basic variable is made to become basic. Note: no need to find the optimal solution, you just have to calculate the cost for the next iteration that related to your discussion. (11 marks) (b) A 400-meter relay race is an event in which teams consist of 4 swimmers (A, B, Cand D) who swim different styles. Suppose that the swimming time (seconds) for each swimmer for 100 meters of breaststroke, freestyle, butterfly, and backstroke are given as follows: Time (seconds) Breaststroke freestyle Butterfly Backstroke 54 55 58 57 52 58 60 55 57 58 60 53 52 54 56 50 A B C D Swimmer Identify the best selection of the swimming style for each swimmer so that the team's time for the race can be minimized. (9 marks) [Total : 25 marks]