What is the lowest cost solution for adding a new plant?

Ultra Corp. is a global laptop manufacturer. It divides its worldwide market into five regions: (1) North America, (2) South America, (3) Asia, (4) Europe, and (5) Africa. The annual demands for these five regions are 128,000, 110,000, 169,000, 111,000, and 78,000 units, respectively. It has determined that a manufacturing plant should have an annual capacity of 300,000 units. The fixed annual costs of maintaining such a manufacturing plant in the five regions are $60 million, $45 million, $50 million, $55 million, and $40 million, respectively. The costs (including production, inventory, transportation, and tariffs) of supplying one laptop from a facility location to a market are shown below. How can the company minimize its facility and supply cost? N30 380 B D E F H G 1 Inputs - Costs, Capacities, Demands Demand Region 2 Production and Transportation Cost per 1,000,000 Units Fixed 3 Facility Location N America S. America Asia Europa Africa Fixed Cost ($) Capacity 4 N America 400 420 450 435 440 60,000,000 300,000 5 S. America 380 355 405 410 400 45,000,000 300,000 6 Asia 390 395 360 375 380 50,000,000 300,000 7 Europe 430 425 415 400 410 55,000,000 300,000 8 Africa 365 370 375 340 40,000,000 300,000 9 Demand 128,000 110,000 169,000 111,000 78,000 10 11 Decision Variables 12 Demand Region - Production Allocation 13 Supply Region N. America S. America Asia Europe Africa Facility Status 14 N. America 15 S. America 16 Asia 17 Europe 18 Africa 19 20 Constraints 21 Facility Locatio. Excess Capacity 22 N. America 23 S. America 24 Asia 25 Europe 26 Africa 27 N. America S. America Europe Asia Africa 28 Unmet Demand 29 30 Objective Function 31 Cost 32 33 34