A multinational corporation is considering establishing distribution hubs in seven strategic locations: Alpha City, Beta Metropolis, Gamma Town, Delta Village, Epsilon City, Zeta Town, and Eta Village. Each hub has the capacity to ship 150 units per week. The weekly fixed cost of operating each hub varies: $1050 for Alpha City, $1110 for Beta Metropolis, $825 for Gamma Town, $750 for Delta Village, $900 for Epsilon City, $690 for Zeta Town, and $660 for Eta Village. The corporation's five major regions have varying demands: 90 units per week for Region A, 80 units per week for Region B, 25 units per week for Region C, 55 units per week for Region D, and 45 units per week for Region E. The production and shipping costs per unit from the hubs to the regions are detailed in Table 1. The objective is to fulfill the weekly demands at the minimum cost, considering the provided information and the following constraints:
I. If the Alpha City hub is opened, then the Beta Metropolis hub must also be opened.
II. At most 4 hubs can be opened.
III. Either the Delta Village or the Epsilon City hub must be opened.
IV. If in both Zeta Town and Eta Village are opened, their fixed opening cost decreases by 15%.
a) Formulate the integer programming (IP) model that can be used to minimize the weekly costs of meeting demand.

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Table 1. Information for the production and shipping costs. From ($) Alpha City Beta Metropolis Gamma Town Delta Village Epsilon City Zeta Town Eta Village To ($) Region A Region B Region C Region D Region E 42 35 35 38 25 38 21 20 23 19 50 18 30 45 37 44 36 25 20 40 27 35 21 21 17 45 37 24 29 30 34 41 40 28 35 Table 1. Information for the production and shipping costs. From ($) Alpha City Beta Metropolis Gamma Town Delta Village Epsilon City Zeta Town Eta Village To ($) Region A Region B Region C Region D Region E 42 35 35 38 25 38 21 20 23 19 50 18 30 45 37 44 36 25 20 40 27 35 21 21 17 45 37 24 29 30 34 41 40 28 35

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Let xi denote the decision to open or close hub i i A B G D E Z and ET with 1 denoting open and 0 de... View the full answer