Midterm Exam

$1.$ SC consulting, a supply chain consulting firm, must decide on the location of its home offices. Its clients are located primarily in the $16$ states listed in Table $5-4.$ There are four potential sites for home offices: Los Angeles, Tulsa, Denver, and Seattle. The annual fixed cost of locating an office in Los Angeles is $$165,428.$ Tulsa is $$131,230,$ Denver is $$140,000,$ and Seattle is $$145,000.$ The expected number of trips to each state and the travel costs from each potential site are shown in the table below. Each consultant is expected to take at most $25$ trips each year.

a$.$ If there are no restrictions on the number of consultants at a site and the goal is to minimize costs, where should the home offices be located and how many consultants should be assigned to each office? What is the annual cost in terms of the facility and travel?