### Instruction:
A university is planning to upgrade its campus-wide Wi-Fi network to accommodate the increasing number of students and devices. The current network can support up to 10,000 simultaneous connections, but the university expects this number to grow by 15% annually over the next five years. To meet this demand, they need to determine the optimal combination of access points, switches, and routers to purchase while staying within their budget of $500,000. Consider the costs of equipment, installation, and ongoing maintenance when making your recommendations.


### Response:

To determine the optimal combination of access points, switches, and routers to purchase while staying within their budget, we first need to calculate the expected number of simultaneous connections in five years.

Current network capacity: 10,000 simultaneous connections
Expected annual growth rate: 15%

Year 1: 10,000 * (1 + 0.15) = 11,500 connections
Year 2: 11,500 * (1 + 0.15) = 13,225 connections
Year 3: 13,225 * (1 + 0.15) = 15,208.75 connections
Year 4: 15,208.75 * (1 + 0.15) = 17,489.06 connections
Year 5: 17,489.06 * (1 + 0.15) ≈ 20,112.42 connections

In five years, the university will need to support approximately 20,112 simultaneous connections. 

Now let's consider the costs of equipment, installation, and ongoing maintenance:

1. Access Points (APs): These devices provide Wi-Fi coverage for users. The more APs installed, the better the coverage and capacity. A good-quality enterprise-grade AP costs around $300 per unit. Each AP can handle about 50-60 simultaneous connections.

2. Switches: These devices connect multiple devices together on a computer network. They are necessary to manage traffic between APs, routers, and wired devices. A decent switch with 24 ports costs around $500, and a 48-port switch costs around $800.

3. Routers: These devices direct data traffic between networks. For a campus-wide network, high-performance routers are needed. A suitable router may cost around $2000 each.

4. Installation and Maintenance: This includes labor costs for installing and configuring the equipment, as well as ongoing maintenance and support. This can vary greatly depending on the size of the campus and complexity of the network, but let's assume a cost of $100,000 for installation and $20,000 per year for maintenance.

Now we need to determine how many access points, switches, and routers are needed:

Access Points: 20,112 connections / 50 connections per AP ≈ 402 APs
Switches: Assuming each switch has 48 ports, 402 APs / 48 ports per switch ≈ 8.375 → 9 switches (to accommodate all APs)
Routers: For simplicity, let's assume 2 high-performance routers will be sufficient for this network.

Cost Breakdown:
- Access Points: 402 APs * $300 = $120,600
- Switches: 9 switches * $800 = $7,200
- Routers: 2 routers * $2,000 = $4,000
- Installation: $100,000
- Maintenance (5 years): $20,000 * 5 = $100,000

Total Cost: $120,600 + $7,200 + $4,000 + $100,000 + $100,000 = $331,800

Based on these calculations, the university should purchase 402 access points, 9 switches, and 2 routers while staying within their budget of $500,000. The total cost, including equipment, installation, and five years of maintenance, is estimated at $331,800.