Microsoft ships its Surface Pro laptops from its assembly plants in China, Thailand and Singapore to its distribution centres (DCs) in Seattle and Minneapolis, before being distributed to the demand centres in the US (Salt Lake City, New York and Austin). The supply, demands, and the handling capacities at each of the distribution centres are given in the tables below. The tables include the respective shipping costs ($/unit) for each origin to destination pair. Assembly Plant 1. China 2. Thailand 3. Singapore Capacities at DCs (number of units) DCs 4. Seattle 5. Minneapolis Demand (number of units) Distribution Centre (DC) 5. Minneapolis $11 $7 $8 2,800 4. Seattle $10 $8 $6 1,500 6. Salt Lake City $6 $8 1,000 Demand Centres 7. New York $9 $11 2,000 Supply (number of units) 1,000 2,000 2,500 8. Austin 12 13 1500 Microsoft wishes to ship as many Surface Pros out of her assembly plants as possible yet minimizing overall shipping costs. Develop an integer programming model to help Microsoft solve this problem: