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 Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in Michigan, Ohio, and California and two in New York.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 "Secures 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: 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. Let x_1 = {1 if data center t is updated 0 if data center t is not updated (b) Solve the model formulated in part (a) to provide a recommendation for management. Optimal solution: Total Cost: $ Millions

Explanation / Answer

The formulation of binary integer programmingmodel that could be used to detrermine the optimal solution to the capacity increase question facing management is as shown below

Min 2.5 x1 +3.5 x2+3.5 x3+4 x4+ 2 x5

subject to

50 x1 +80 x2+40 x3+90 x4+ 20 x5 >= 90

30 x1 +40 x2+80 x3+60 x4+ 30 x5 >= 90

x1 ,x2, x3, x4, x5 = 0,1

Solution of the formulated problem is as follows

Total cost = $6 million

Solver Solution

X1 X2 X3 X4 X5 Total Demand

Decision Variables 1 0 1 0 0

Cost 2.5 3.5 3.5 4 2 6

Constrain 1 50 80 40 90 20 90 90

Constrain 2 30 40 80 60 30 110 90

b) By solving using simplex method (the solution is too big too write or upload here,if u still need reply me i will upload the detail solution) we get the optimal solution as

x1=0, x2=0, x3=9/16, x4=3/4, x5=0

Minimize Z = 4.9688

Hope u got the answer,if u have any problem comment in here i will reply.

Thank you

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.