To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of fruit smoothies made,
- $x_2$ as the number of vegetable smoothies made.

The profit per fruit smoothie is $4, and the profit per vegetable smoothie is $5. Thus, the objective function to maximize profit can be represented as:
\[ \text{Maximize:} \quad 4x_1 + 5x_2 \]

Given the constraints:
- Each fruit smoothie takes 5 minutes on the cutting machine and 5 minutes on the blending machine.
- Each vegetable smoothie takes 7 minutes on the cutting machine and 4 minutes on the blending machine.
- Both machines are available for at most 400 minutes per day.

We can represent these constraints as:
\[ 5x_1 + 7x_2 \leq 400 \] (Cutting machine constraint)
\[ 5x_1 + 4x_2 \leq 400 \] (Blending machine constraint)

Also, since we cannot make a negative number of smoothies, we have:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of fruit smoothies'), ('x2', 'number of vegetable smoothies')],
    'objective_function': '4*x1 + 5*x2',
    'constraints': ['5*x1 + 7*x2 <= 400', '5*x1 + 4*x2 <= 400', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

# Create a new model
m = Model("Smoothie_Optimization")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="fruit_smoothies")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="vegetable_smoothies")

# Set the objective function
m.setObjective(4*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 7*x2 <= 400, "cutting_machine")
m.addConstr(5*x1 + 4*x2 <= 400, "blending_machine")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of fruit smoothies: {x1.x}")
    print(f"Number of vegetable smoothies: {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```