Please solve using LINGO and provide explanations.
Project-4 QBA775- Quantitative Methods Due-05-7-2021 at 11:59 PM • You can discuss this lab-work with any other student in the class. • You can get help or clarification from the instructor. • For each question, you need to fully interpret your results. Your report should be typed. • You can upload your lab-work file under lab assignment folder in Blackboard. • Late submission is not accepted. • You are supposed to upload LINGO output in blackboard. 1. Cloud Services Capacity Planning. Galaxy Cloud Services operates several data centers across the United States containing servers that store and process the data on the Internet. Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in Michigan, Ohio, and California and two in New York. Management is considering increasing the capacity of these data centers to keep up with increasing demand. Each data center contains servers that are dedicated to Secure data and to Super Secure data. The cost to update each data center and the resulting increase in server capacity for each type of server are as follows: Data center Cost($millions) Secure Servers Super Secure Servers Michigan 2.5 50 30 New York 1 3.5 80 40 New York 2 3.5 40 80 Ohio 4 90 60 California 2 20 30 The projected needs are for a total increase in capacity of 90 Secure servers and 90 Super Secure servers. Management wants to determine which data centers to update to meet pro- jected needs and, at the same time, minimize the total cost of the added capacity. In particular you have been asked to (a) Formulate a binary integer programming model that could be used to determine the optimal solution to the capacity increase question facing management. (b) Solve the model formulated in part (a) to provide a recommendation for management. 1 2. Hub Location at Western Airlines Western Airlines has decided that it wants to design a hub system in the United States. Each hub is used for connecting flights to and from cities within 1000 miles of the hub. Western run flights among the following cities: Atlanta, Boston, Chicago, Denver, Houston, Los Angeles, New Orleans, New York, Pittsburgh, Salt Lake City, San Francisco, and Seattle. The company wants to determine the smallest number of hubs it will need to cover all of these cities, where a city is ”covered” if it is within 1000 miles of at least one hub. The following table lists the cities that are within 1000 miles of other cities. Cities Cities within 1000 Miles) Atlanta(AT) AT,CH,HO,NO,NY,PI Boston(BO) BO, NY, PI Chicago(CH) AT,CH,NY,NO,PI Denver(DE) DE, SL Houston(HO) AT, HO, NO Los Angeles(LA) LA,SL,SF New Orleans(NO) AT,CH,HO,NO New York(NY) AT, BO, CH, NY, PI Pittsburgh(PI) AT, BO, CH, NY, PI Salt Lake City (SL) DE LA, SL, SF, SE San Francisco (SF) LA, SL, SF, SE Seattle(SE) SL, SF, SE Formulate and solve a linear binary model to find the minimum number of hub locations that can cover all cities. Please name those cities location which will cover all cities. Note Since all the cities are binary, binary is the requirement for this problem. So you are supposed to use @BIN(AT); @BIN(BO); ......@BIN(SE); 2