Please show steps in a systematic format, i.e. step 1, step 2, step 3 and so on. Thank you!

GreeTech, Inc., is a manufacturer of air conditioners that has seen its demand grow significantly. The company anticipates nationwide demand for the next year to be 190,000 units in the South, 140,000 units in the Midwest, 110,000 units in the East, and 100,000 units in the West. Managers at GreeTech are designing the manufacturing network and have selected four potential sites-New York, Atlanta, Chicago, and Dallas. Plants could have a capacity of either 200,000 or 400,000 units. The annual fixed costs at the four locations are shown in the following Table, along with the cost of producing and shipping an air conditioner to each of the four markets. (a) Develop the formula of optimization model to find out where should GreeTech build its factories and how large should they be. Specify decision variables, objective function, and constraints based on the given data/information. (Solving in Excel Not required) (10 points) (b) If, for customer service reasons, each market receives all shipments from a single DC, how will the model change from (a)? Show the model formula. (Solving in Excel Not required) (7 points)