Linear Programming/ Transportation/ Assignment Problem

2. BudgetCloud is embarking on a project to build a datacenter which will house its public, retail, low, middle, and high income server racks. The low, middle and high income racks host applications built by BudgetCloud, while the retail and public racks are rented to businesses and the general public respectively. Their datacenter must also include security section to monitor network traffic. The size this section (number of racks) is proportional to the amount of network traffic (measured in GBs). Similarly, the amount of retail racks is proportional to the number of public, security, low, mid, and high income racks. The following table provides the pertinent data of the situation: The security section can occupy a maximum of 2m2 and its monitoring capacity is limited to 25 GB per seruirty server rack. The operating annual cost per security server rack is $10,000. The datacenter will be located on a 50m2 vacant basement owned by the company. Adjacent to the basement are 200 empty storage rooms. Each room is .25m2 and can be refurbished for use at a cost of $7000. Open space, offices, and aisles consume 15% of total available space. (a) Formalize the above as an optimization problem. State any assumptions made. [15 marks] 2. BudgetCloud is embarking on a project to build a datacenter which will house its public, retail, low, middle, and high income server racks. The low, middle and high income racks host applications built by BudgetCloud, while the retail and public racks are rented to businesses and the general public respectively. Their datacenter must also include security section to monitor network traffic. The size this section (number of racks) is proportional to the amount of network traffic (measured in GBs). Similarly, the amount of retail racks is proportional to the number of public, security, low, mid, and high income racks. The following table provides the pertinent data of the situation: The security section can occupy a maximum of 2m2 and its monitoring capacity is limited to 25 GB per seruirty server rack. The operating annual cost per security server rack is $10,000. The datacenter will be located on a 50m2 vacant basement owned by the company. Adjacent to the basement are 200 empty storage rooms. Each room is .25m2 and can be refurbished for use at a cost of $7000. Open space, offices, and aisles consume 15% of total available space. (a) Formalize the above as an optimization problem. State any assumptions made. [15 marks]