The PQR Auto Parts Company has 12 retail stores in the city of Springdale. The PQR Company is planning to build a new warehouse to service its retail stores. The locations of the stores and the expected deliveries per week from the warehouse to each store are given below. Assume travel within Springdale is rectilinear and that the delivery truck returns to the warehouse after each delivery to a store.

a. If there are no restrictions on the warehouse location, where should it be located in order to minimize the distance traveled each week?

b. If the PQR Company is going to include a new retail outlet at the warehouse location, where should it be located if it cannot be within 1 rectilinear mile of an existing store?

c. Where should the warehouse be located in order to minimize the distance between it and any store?

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Store Location (miles) Expected Deliveries (4, 2) 123456789012 1 (4,5) 1 (5,2) 1 (5, 1) 1 (2, 2) 3 (2, 3) 5 (2, 4) (2,5) (1, 0) (0, 1) (0, 3) (3,2) 6 2 4123 3