Minfly Golf Company manufactures golf balls at Philadelphia, Chicago, and Denver. Cases of golf balls are shipped to warehouses in Orlando, Dallas, and Los Angeles. The following table provides the weekly capacities of the factories and the minimum weekly requirements of the warehouses along with the cost per case to ship between them. Which shipping plan will minimize total costs?
Factories Orlando Dallas Los Angeles Capacities
Philadelphia 6 9 16 2500
Chicago 7 5 10 1500
Denver 13 8 5 2000
Requirements 3000 1200 1800
After the #1 player on the tour started using Minfly balls, demand from the three warehouses has increased by 1,000 cases per week. To meet this increased demand, an additional factory needs to be built with a capacity of 3,000 cases per week. The two potential locations being considered are Memphis and San Francisco. The cost per case to ship between these locations and the warehouses are as follows:
Factories Orlando Dallas Los Angeles Capacities
Memphis 6 4 12 3000
San Francisco 13 8 5 3000
Requirements 4000 2200 2800
Where should the new factory be located?