Please solve the following operational research problem. Please show all work for the whole problem. Please do not use excel handwritten work is preferred.

4. CIP has three electric power plants that supply the power needs of four cities. Each power plant can supply the following numbers of kilowatt-hours (kwh) of electricity: plant 1, 35 million; plant 2, 50 million; plant 3, 40 million. The peak power demands in these cities, which occur at the same time (2:00 P.M.), are as follows (in kwh): city A, 20 million; city B, 20 million; city C, 30 million; city D, 30 million. The costs of sending 1 million kwh of electricity from plant to city depend on the distance the electricity must travel. The following is the cost table. Plant 1 Plant 2 Plant 3 City A $ 8 $ 9 $ 14 City B $6 $12 $9 City C $10 $13 $ 16 City D $ 9 $ 7 $ 5 Assuming the goal is to minimize the cost of sending electricity while meets each city's peak power demand. a) Formulate a balanced transportation problem that can be used to determine how the electricity should be sent. b) Use the northwest-corner method to find a basic feasible solution c) Use the minimum-cost method to find a basic feasible solution. d) Use the Vogel's method to find a basic feasible solution, e) Use the result of part (c) to find an optimal solution