Problem 2 (Adapted from Winston, 2004): A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse open is $400 for New York, $500 for Los Angeles, $300 for Chicago, and $250 for Atlanta. Region 1 of the country requires 50 units per week, region 2 requires 90 units per week, and region 3 requires 40 units per week. The costs (including production and shipping costs) of sending one unit from a plant to a region are shown in the following table: From Region 3 New York Los Angeles Chicago Atlanta 60 To ($) Region 2 50 70 55 46 Region 1 24 35 18 44 30 25 54 We want to meet weekly demands at a minimum cost, subject to the preceding information and the following restrictions: 1. If the New York warehouse is closed, then the Los Angeles warehouse must be opened. 2. At most three warehouses can be opened. 3. Either the Atlanta or the Los Angeles warehouse must be opened. Part a: Formulate an integer-linear program to minimize the weekly costs of meeting demand. Part b: Solve the problem using AMPL/CPLEX and report the obtained optimal solution. Include a typed version of your AMPL model file and/or data file and your AMPL session in your submission. Problem 3: The IE Department wants to LIVIU GUTSUTON STRI, ECON, and Simulation) among three Part a: Formulate an ILP whose solution will tell us how to minimize total costs. Part b: Solve the problem using AMPL/CPLEX and report the obtained optimal solution. Include a typed version of your AMPL model file and/or data file and your AMPL session in your submission