## Problem Description and Formulation

The problem is an optimization problem with two variables: 'SOC operators' and 'network administrators'. The objective is to minimize the function $9 \cdot SOC^2 + 6 \cdot Admin^2$.

The problem has several constraints based on the attributes of 'SOC operators' and 'network administrators':

- **Network Latency Impact**: SOC operators add 0.86 ms and network administrators add 0.09 ms. The total must be at least 20 ms.
- **Data Accessibility Impact**: SOC operators have an impact of 0.64 and network administrators have an impact of 0.79. The total impact must be at least 13, and the sum of their squared impacts must be at least 13 and at most 32.
- **Cost**: SOC operators cost 0.34 dollars and network administrators cost 0.12 dollars. The total cost must be at least 23 dollars.
- **Additional Constraints**: 
  - $7 \cdot SOC^2 - 6 \cdot Admin^2 \geq 0$
  - The network latency impact squared must be at most 76 ms.
  - The total cost squared must be at most 68 dollars.
  - Both SOC operators and network administrators must be whole numbers.

## Gurobi Code Formulation

```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
SOC = m.addVar(name="SOC_operators", vtype=GRB.INTEGER)
Admin = m.addVar(name="network_administrators", vtype=GRB.INTEGER)

# Objective function
m.setObjective(9 * SOC**2 + 6 * Admin**2, GRB.MINIMIZE)

# Constraints
m.addConstr(0.86 * SOC + 0.09 * Admin >= 20, name="network_latency_constraint")
m.addConstr(0.64 * SOC + 0.79 * Admin >= 13, name="data_accessibility_constraint")
m.addConstr((0.64 * SOC)**2 + (0.79 * Admin)**2 <= 32, name="data_accessibility_squared_constraint")
m.addConstr(0.34 * SOC + 0.12 * Admin >= 23, name="cost_constraint")
m.addConstr(7 * SOC**2 - 6 * Admin**2 >= 0, name="additional_constraint_1")
m.addConstr((0.86 * SOC)**2 + (0.09 * Admin)**2 <= 76, name="network_latency_squared_constraint")
m.addConstr((0.34 * SOC + 0.12 * Admin)**2 <= 68, name="cost_squared_constraint")

# Solve the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"SOC operators: {SOC.varValue}")
    print(f"Network administrators: {Admin.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```