An energy company has 3 power plants that supply electricity to 3 different city grids. The electricity supply of each power plant and the electricity demand amounts of the cities are given in the table below. In addition, the transportation costs that occur depending on the distances are also shown in the table. a) Write the linear programming model of the problem. (20 points) b) Find the initial solution using the northwest method and interpret the solution. (20 points)

	city 1	city 2	city 3	supply
plant 1	$8	$6	$10	35
plant 2	$9	$12	$13	30
plant 3	$14	$9	$16	80
Demand	55	50	40