## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables as follows:
- $x_1$ represents the units of ice cream produced
- $x_2$ represents the units of cheese produced

The objective is to maximize profits, with the profit per unit of ice cream being $2.5 and the profit per unit of cheese being $4. Therefore, the objective function can be represented as:

Maximize: $2.5x_1 + 4x_2$

The constraints based on the given information are:
- The ice cream team can produce at most 50 units of ice cream per day: $x_1 \leq 50$
- The cheese team can produce at most 80 units of cheese per day: $x_2 \leq 80$
- The shared processing machine can process at most 100 units of total items per day: $x_1 + x_2 \leq 100$
- Non-negativity constraints, as the units produced cannot be negative: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'ice cream'), ('x2', 'cheese')],
    'objective_function': '2.5*x1 + 4*x2',
    'constraints': [
        'x1 <= 50',
        'x2 <= 80',
        'x1 + x2 <= 100',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="ice_cream", lb=0, ub=50, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="cheese", lb=0, ub=80, vtype=gp.GRB.CONTINUOUS)

# Define the objective function
model.setObjective(2.5 * x1 + 4 * x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(x1 <= 50, name="ice_cream_production_limit")
model.addConstr(x2 <= 80, name="cheese_production_limit")
model.addConstr(x1 + x2 <= 100, name="total_production_limit")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Ice Cream Production: {x1.varValue}")
    print(f"Cheese Production: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("The model is infeasible or has no solution.")
```