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4. (17 points) A company is determining the locations of new warehouses which provide products to its three supermarkets. The locations of those supermarkets (a,b) and the amount of product transportations are provided in the following table. The distance unit is kilometer (km). The fixed daily operating cost at one warehouse is $17,000/day, and the transportation cost is $1/kg/km. All the distances are calculated rectilinearly. (a) (15 points) Find the number of warehouses and their locations to minimize the daily cost. (b) (2 points) Calculate the lowest daily cost. a b Demand of transportation Supermarket 1 0 0 2000 kg/day 2 20 0 1000 kg/day 3 30 0 1200 kg/day