Galaxy Cloud Services operates several data centers across the United States tha

Question

Galaxy Cloud Services operates several data centers across the United States that contain servers which 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 Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in Michigan, Ohio, and California and two in New York.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 is as follows: Data Center Cost ( millions) Secure Servers Super Secure Servers Michigan New York 1 New York 2 Ohio California 3.5 3.5 4.0 2.0 50 80 40 90 20 30 40 80 60 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 projected needs and, at the same time, minimize the total cost of the added capacity (a) Formulate a binary integer programming model that could be used to determine the optimal solution to the capacity increase question facing management. If required, round your answers to one decimal place 1 if data center i is updated 0 if data center i is not updated Let& = Min 2.5 3.5 X2 3.5 4 2 s.t. 50 80 40 X3 90 20 90Super Secure 30 40 80 X3 60 30 90 Secure X1, X2, X3, X4, X5 0,1 (b) Solve the model formulated in part (a) to provide a recommendation for management. Optimal solution x1 = 0, x2 = 1, x3 = 0, x4 1, x5 = 0 Total Cost: 7.7 Millions

Explanation / Answer

Min 2.5x1 + 3.5x2 + 3.5x3 + 4x4 + 2x5
s.t.
30x1 + 40x2 + 80x3 + 60x4 + 30x5 >= 90 (Super Secure)
50x1 + 80x2 + 40x3 + 90x4 + 20x5 >= 90 (Secure)

Optimal solution: x1=0, x2=0, x3=0, x4=1, x5=1
Total cost = $6 millions

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