Problem 2 135 points]: Eastinghouse sells air conditioners. The annual demand for air conditioners in each region of the country is as follows: East, 100,000; South, 150,000; Midwest, 110,000; and West, 90,000. Eastinghouse is considering building its air conditioners in four different cities: New York, Atlanta, Chicago, and Los Angeles. The cost of producing an air conditioner in a city and shipping it to a region of the country is given as follows: From To East New York $206 Atlanta $225 Chicago $230 Los Angeles $290 South Midwest West $225 $230 $290 $206 $221 $270 $221 $208 $262 $270 $262 $215 Any factory can produce up to 150,000 air conditioners per year. The annual fixed cost of operating a factory in each city is given by: New York, $6,000,000; Atlanta, $5,500,000; Chicago, $5,800,000; Los Angeles, $6,200,000. At least 50,000 units of the Midwest demand for air conditioners must come from New York, and at least 50,000 units of the Midwest demand must come from Atlanta. a) Define the decision variables and write down the detailed mathematical formulation of Eastinghouse's optimization problem to minimize its total cost. [15 points) b) Solve the optimization problem by Excel Solver. [15 points) c) What are Eastinghouse's optimal decisions and minimal cost of meeting demand for air conditioners? (5 points)