Transportation Cost Distribution Centers 1 100 50 100 Capacity of the Manufacturing Plant 200 180 120 160 Fixed Operating Costs 1.200 1.000 900 1.400 Manufacturing Plants | |N 3 200 50 100 80 100 200 200 100 300 4 Demand 150 120 90 1. Keep all the plants and find the best transportation plan: a) Provide the mathematical model of the problem. (Sets, Parameters, Decision Variables, Objective Function and Constraints) b) Present your optimal solution. (Total cost, fixed costs, transportation costs and transportation plan) 2. Do we need all the plants? Which plants to close? In part 1, it is expected that all the facilities are opened. However, DLM also wants to consider to close some of the plants. What will be the optimal solution to minimize overall (fixed + transportation) costs? Modify your mathematical model and find the least costly solution. Do not forget to explain your model and modifications. Present your optimal solution and compare the solutions of Parts 1 and 2. 3. Economic considerations in charge: DLM realized that a plant should produce at least 80 units once it is opened. (Keep that in mind, total demand is 360 units). Otherwise such an investment is not economical in the long run. Modify your mathematical model and find the least costly solution. Do not forget to explain your model and modifications. Present your optimal solution and compare the solutions of Parts 2 and 3