YOU DO NOT NEED TO SOLVE THE RESULTING OPTIMIZATION PROBLEM. You only need to define the notation, present the complete formulation, and then explain how solutions from solving the optimization problem can be used to answer the question.

Drylce is a manufacturer of air conditioners that has seen its demand grow significantly. The company anticipates nationwide demand for the next year to be 180,000 units in the South, 120,000 in the Midwest, 110,000 in the East, and 100,000 units in the West. Managers at Drylce are designing the manufacturing network and have selected four potential sites - New York, and Atlanta, Chicago, and San Diego. Plans could have a capacity of either 200,000 or 400,000 units. The annual fixed cost at the four locations are shown in Table 2, along with the cost of producing and shipping an air conditioner to each of the four markets. Where should Drycle build its factories and how large should they be? Table 2: Production and transport costs for Drylce New York Atlanta Chicago San Diego Annual foed cost of 200,000 plant 56 million $5.5 million $5.6 million 56.1 million Annual foved cost of 400,000 plant $10 million $9.2 million $9.3 million $10.2 million East $211 $232 $238 $299 South S232 $212 $230 $280 Midwest S240 $230 $215 $270 West $300 $280 $270 $225