DataTech is embarking on a project to build a data center that will house its low, middle, upper, public, and retail server racks. The low, middle, and high-income racks host applications built by DataTech, while the retail racks are rented to businesses, and public racks are rented to the general public. Their data center must also include a security section to monitor network traffic. The size of 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 data on the situation:

	Low income unit	Middle income unit	Upper income unit	Public income unit	Security Unit	Retail Unit
Minimum	100	125	75	300		0
Maximum	200	190	260	600		25
Physical Space (m2)	0.05	0.07	0.03	0.025	0.045	0.1
Average network traffic (GBs)	1.3	1.2	0.5	1.4
Retail demand per unit (racks)	0.023	0.034	0.046	0.023	0.034
Annual income ($)	7,000	12,000	20,000	5,000	-	15,000

The security section can occupy a maximum of 2m^2, and its monitoring capacity is limited to 25GB per security server rack.

The operating annual cost per security server rack is $10,000.

The data center will be located on a 50m² vacant basement owned by the company. Adjacent to the basement is 200 empty storage rooms.

Each room is 0.25 m² and can be refurbished for use at the cost of $7000. Open space, offices, and aisles consume 15% of the total available space.

a) Formalize the above as an optimization problem. State any assumptions made.