1. Formulate and solve a model to determine the total cost (shipping and fixed) of an optimal distribution plan that uses all plants. That is, in this model, all plants are open and all fixed costs are incurred.
2. Formulate and solve a model to assist the company in determining which plants should remain open and which should be closed. What plants should remain open?
   1. Plant 1
   2. Plant 2
   3. Plant 3
   4. Plant 4
   5. Plant 5
3. What is the total cost for the optimal solution to the model that selects plants to remain open?
4. What is the change in shipping cost between the solution with all plants open versus the solution found with the model that selects some plants to be opened and some plants to be closed?
   1.  

A company is unsure about the future demand for a product that it is producing in five different plants. The company is considering reducing its fixed operating costs by closing one or more plants, even if this means incurring in an increase in transportation costs. The relevant costs for the problem are provided in the following table. Transportation costs to warehouses Fixed Plant A B C D Capacity cost 1 $56 $21 $32 $65 12 $2,100 2 $18 $46 $7 $35 18 $850 3 $12 $71 $41 $52 14 $1,800 4 $30 $24 $61 $28 10 $1,100 5 $45 $50 $26 $31 16 $900 Demand 6 14 8 10 Estimated demand and capacity are given in thousands of units. Transportation costs are given in thousands of dollars to transport one thousand units. Annual fixed costs are given in thousands of dollars. (There is no need to convert any of the units, use the values as they are.)