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: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 30,000 Toledo Denver Kansas City $300,000 40,000 $375,000 10,000 $500,000 20,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston Atlanta Houston 30,000 20,000 20,000 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 2 St. Louis 8 4 3 (a) Develop 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. Solve the model and answer the following questions. What is the optimal cost? What is the optimal set of plants to open? Toledo (b) Using equation 12.1, find a second-best solution. What is the optimal set of plants to open? Detroit & Toledo What is the increase in cost versus the best solution from part (a)? (12.1 Equation) Step 1: Solve the original problem Step 2: Create two sets: O = the set of variables equal to one in Step 1 Z = the set of variables equal to zero in Step 1 Step 3: Add the following constraint to the original problem, and solve (Sum of variables in the set O) - (Sum of variables in the set Z) < (number of variables in the set O) - 1