Note: Please do A, B, and C on paper only , and D using LINGO

Powerco has three electric power plants that supply the needs of four cities. Each power plant can upply the following numbers of kWhr of electricity: Plant 1-60 million; Plant 2-50 million; Plant 3-40 illion. The peak power demands in these cities, which occur at the same time, are as follows (in kWhr): ity 1-30 million; City 2-50 million; City 3-30 million; City 4-40 million. The costs of sending 1 illion kWhr of electricity from the plant to the city depend on the distance the electricity must travel (see Table). Formulate an LP problem to minimize the cost of meeting each city's peak power demand. City 1 From Plant 1 Plant 2 Plant 3 $8 City 2 6 12 9 To City 3 10 13 16 City 4 9 7 5 9 14 A. Formulate this problem (write down decision variable objective function and constraints) B. Use the northwest corner method, minimum cost method, and vogles method to find BFS C. Use transportation simplex to find the Optimal solution D. Use LINGO to find the optimal solution and verify our solution in part C