2. Budget Cloud 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 Budget Cloud, 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 perti- nent data of the situation: Low Middle Upper Public Security Retail income income income unit unit unit unit unit unit Minimum 100 125 75 300 0 Maximum 200 190 260 600 25 Physical space (m2) .05 .07 .03 .025 .045 .1 Average network 1.3 1.2 .5 1.4 traffic (GBS) Retail demand per .023 .034 .046 .023 .034 unit (racks) Annual income ($) 7,000 12,000 20,000 5,000 15,000 The security section can occupy a maximum of 2 m and its monitoring capac- ity 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 50 m vacant basement owned by the company. Adjacent to the basement are 200 empty storage rooms. Each room is .25 m 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]