The company wants to distribute the items with minimum cost by having an efficient logistics network. Table $1$ includes required information for the problem setting. Please answer the following questions according to the explanations below by preparing a report. $1.$ 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. 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?