Question: QUESTION 2 Total: 25 Marksl a) Lexus company has three manufacturing plants and three distribution centres. The supply at each of the plant and the

QUESTION 2 Total: 25 Marksl a) Lexus company has

QUESTION 2 Total: 25 Marksl a) Lexus company has three manufacturing plants and three distribution centres. The supply at each of the plant and the demand at the each of the distribution centre with the cost per unit for each of the route are as follows: TO Store 1 Store 2 Store 3 Supply FROM Plant 1 Plant 2 Plant 3 Demand $12 9 20 25 20 11 14 50 15 4 8 45 60 15 55 i. Use North-west corner method to find an initial solution and then apply the Stepping-Stone method to find the least-cost distribution system. Then, determine the minimum total cost. [12 marks] ii. Is there any alternate optimal solution? Why? [3 marks) b) Prof Mulan is assigning lecturers to subjects for the next trimester. The past three years failure rate is the main criterion for deciding who should teach each subject. The failure rates of each subject taught by each lecturer are shown in the following table: Lecturer Subject Dr. Lim Dr. Chong Dr. Cindy Dr. Jenny Statistics / 15 12 15 16 Statistics II 12 11 14 13 Research Methodology 14 10 13 17 Business Mathematics 11 13 12 15 Determine all (if more than one) optimal assignment(s) of lecturers to subjects to minimise the overall failure rate. What is the overall failure rate? 110 marks

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