A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse open is $400 for New York, $500 for Los Angeles, $300 for Chicago, and $150 for Atlanta. Region 1 of the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs of sending 1 unit from a warehouse to a region are shown in the following table:

We wish to meet weekly demands at minimum cost, subject to the preceding information and the following restrictions:
1. If the New York warehouse is opened, then the Los Angeles warehouse must be opened.
2. At most three warehouses can be opened.
3. Either the Atlanta or the Los Angeles warehouse must be opened.
a) Develop a linear programming formulation for this problem based on the following restrictions.
b) Find the solution utilizing Transportation Method with either Least-unit cost or North-west algorithm.

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To FROM Region 2 Region 3 Region 1 New York 20 40 50 Los Angels 48 15 26 Chicago 35 18 26 35 Atlanta 24 50