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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 Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in Michigan.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 arc as follows: 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. Formulate a binary integer programming model that could be used to determine the optimal solution to the capacity increase question facing management. Solve the model formulated in part a to provide a recommendation for management.
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Sagot :

Decision Variables

Out of the given five outdated data centers, the question raised is about-- which are to be upgraded so as meet the conditions at the minimal possible cost.

Let X1, X2, X3, X4 and X5 represents the variables corresponding to data centers at Michigan, New York 1, New York 2, Ohio and California independently. These variables can take the double values of zero( not named for upgradation) or one( in case named for upgradation).

Ojective function

As mentioned in the history and submitted above the ideal is to minimize the total cost of the added capacity.

The total cost of added capacity in terms of the below mentioned decision variables is given as follows

Minimize Z = 2.5 X13.5 X23.5 X3 4X4 2X5

The constraint is about the vacuity and demand for the total increase in capacity of 90 Secure waiters and 90 Super Secure waiters. In terms of decision variables the constraints are as follows

50X1 80X2 40X3 90X4 20X5> = 90( Secure waiters)

30X1 40X2 80X3 60X4 30X5> = 90( Super Secure waiters)

Eventually X1, X2, X3, X4, X5 are double.

The optimal result is as follows. Upgrade Michigan and New York 2 data centers with total cost of$ 6 millions.

To know more about decision variables, click on the link below:

https://brainly.com/question/15233471

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