d) Table 1 shows the initial tableau a normal minimization LP problem, with two decision variables (i.e. x1, x2 ) and three slack variables (i.e. S1, S2, S3). Table 1: Z S2 X2 1 RHS S1 0 S3 0 0 X1 1 -2 -3 -1 0 -6 OOO -1 1 -7 -1 -3 0 1 -8 Determine its optimal solution using the dual simplex method. Also give optimal solution to the dual variables. (15) QUESTION 4 [37] a) A Power company has three plants that supply the need of three cities (as shown in Table 2). Each plant can supply the following numbers of kWh of electricity. Plant 1, 2 and 3 can supply 30, 40 and 50 million kWh, respectively. The demand at city 1, 2 and 3 are 20, 40 and 40, respectively. The cost of sending electricity from each plant to each city depends on the distance the electricity must travel. Table 2: To Plant 1 Plant 2 Plant 3 Transportation costs From City 1 City 2 10 11 8 14 7 10 City 3 16 11 13 i) Determine the initial basic feasible solution using the Minimum Cost Method. ii) Use the stepping stone method to find the optimal solution. (5) (12) b) Five employees are available to perform four jobs. The time it takes each person to perform each job is given in Table 3. Table 3: Persons Person 1 Person 2 Person 3 Person 4 Person 5 IT Time Job 2 Job 3 18 30 27 20 28 22 25 Job 1 22 18 26 16 21 Job 4 18 22 28 14 28 4 Page 4/5 SSOA021 JULY EXAMINATION 2021 Using the Hungarian Method, determine the assignment of employees to jobs that minimize the total time required to perform the four jobs