Please Answer all parts clearly in same format as above for thumbs up and good rating. Thanks!!

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 $200,000 10,000 2 Toledo $275,000 20,000 3 Denver $400,000 30,000 4 Kansas City $475,000 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 2 Atlanta 30,000 3 Houston 30,000 The shipping cost per unit from each plant to each distribution center is as follows. Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 N St. Louis 00 4 3 (b) Solve the model you formulated in part (a). What is the optimal cost in $)? $ What is the optimal set of plants to open? (Select all that apply.) O Detroit Toledo O Denver Kansas City (c) Using equation (13.1), (Sum of variables in the set o) - (sum of variables in the set z) S (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 cost (in $) versus the best solution from part (b)? $