Two reservoirs are available to supply water for the needs of three cities. Each reservoir can supply 50 million gallons of water per day. Each city requires 40 million gallons of water per day. For every shortfall of one million gallons per day, there is a fine to be paid. For city A, the fine is IDR 200,000; for city B, the fine is IDR 220,000, and for city C, it is IDR 230,000. The cost (in rupiah) for transporting from the reservoir to each city per million gallons of water is as shown in the following table:
Question:
Formulate this problem into a transportation table, then find a basic initial feasible solution using the Vogel approach method.
To City B: 80,000 70,000
From Reservoir 1 Reservoir 2
City A: 70,000 90,000
City C: 100,000 80,000