business analytics mixed integer programming model question

The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units, Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Plant Number Proposed Plant Annual Fixed cost Annual Capacity 1 Detroit 10,000 $200,000 $275,000 Toledo 20,000 3 Denver 30,000 $400,000 $525,000 4 Kansas City 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows. Distribution Center Number Distribution Center Annual Demand 1 Boston 20,000 Atlanta 30,000 Houston 10,000 The shipping cost per unit from each plant to cach distribution center is as follows Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 2 3 3 Toledo 4 3 4 Denver 9 7 5 10 4 2 Kansas City St. Louis 8 8 4 3 (a) Formulate a mixed Integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand and minimize total cost in thousands of dollars). (Let x = units shipped in thousands from plant to distribution center with the existing plant in St. Louis being plant number 5. Let - it a plant is constructed Detroit and if not. 1 a plant is constructed in Toledo and or not. Y Lira plant is constructed in Denver and it not, and ita plant is constructed in Kansas Chy and of mot.) Min st Detro Capacity X Toledo Capacity x Denver Capacity X Kansas City Capacity St. Louis Capacity X Boston Demand x Atlanta Demand X Houston Demand X Xy for all and I and Y... binary (b) solve the model you formulated in part (a). What is the optimal cost (ins? $ What is the optimal set of plants to open? (Select an that apply) Detroit Toledo Denver Kansas City ( Using equation (13.1). (Sum of variables in the set o) - (sum of variables in the set 27 (number of variables in the set o) - 1 where is the set of binary variables in our original optimal solution set to one and Z is the set of those set to zero, find a second best solution. What is the increase in cont best solution from part (b)? S) versus the