YOU DO NOT NEED TO SOLVE THE RESULTING OPTIMIZATION PROBLEM. You only need to define the notation, present the complete formulation, and then explain how solutions from solving the optimization problems can be used to answer questions.

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 1. 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 (home office) are shown in Table 1 as well. We assume that each consultant in a home office makes at most 25 trips to clients 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 (you can model it as a continuous or discrete variable) should be assigned to each office? What is the annual cost in terms of the facility and travel? b) If at most 10 consultants are to be assigned to a home office, where should the offices be set up? How many consultants should be assigned to each office? What is the annual cost of this network? c) Revise your formulation in a) by assuming that each state must be served exclusively by a single home office. Do you think the total cost will increase or decrease? Why? Table 1: Travel costs and number of trips for SC consulting Travel Costs (5) State Los Angeles Tulsa Denver Seattle Number of Trips Washington 150 250 200 25 40 Oregon 150 250 200 75 35 California 75 200 150 125 100 Idaho 150 200 125 125 25 Nevada 100 200 125 150 40 Montana 175 175 125 125 25 Wyoming 150 175 100 150 50 Utah 150 150 100 200 30 Arizona 75 200 100 250 50 Colorado 150 125 25 250 65 New Mexico 125 125 75 300 40 North Dakota 300 200 150 200 30 South Dakota 300 175 125 200 20 Nebraska 250 100 125 250 30 Kansas 250 75 75 300 40 Oklahoma 250 25 125 300 55