1. Three electric power plants with capacities of 25, 40, 15, and 30 million kWh supply electricity to four cities. The maximum demands at the three cities are estimated at 30, 40, 35, and 25 million kWh. The price per million kWh at the four cities is given in Table. There is a penalty for each unmet city unit of demand. With city 1, a penalty cost of $950 is incurred; with city 2, $800; with city 3 $900 and with city 4. $1100.The utility company wishes to determine the most economical plan for the distribution of energy. Cityl City2 City3 City4 Plant $600 $700 $750 $400 Plant2 $450 $650 $800 $500 Plant3 $320 $300 $675 $450 Plant4 $500 $480 $700 $450 Answer these questions according to problem given above. a) Set up balanced mathematical model. b) Create transportation table. c) Solve this problem by using north-west method. d) Solve this problem by using minimum-cost method. e) Select non-improved solution that you found, try to reach optimal value by using transportation simplex method. f) Compare the results that you found and try to explain the differences. Which algorithms are more efficient or not?