## Step 1: Define the symbolic representation of the problem
Let's denote the number of red umbrellas as $x_1$ and the number of blue umbrellas as $x_2$. The objective is to maximize profit, which is $3x_1 + 5x_2$. The constraints are:
- The total number of umbrellas is at most 100: $x_1 + x_2 \leq 100$
- At least 10 umbrellas are red: $x_1 \geq 10$
- At least 4 times as many customers prefer blue umbrellas to red umbrellas: $x_2 \geq 4x_1$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

However, since we are dealing with physical items (umbrellas), we can reasonably assume $x_1 \geq 0$ and $x_2 \geq 0$ are implicitly satisfied by the other constraints.

## 2: Write down the symbolic representation in the required format
```json
{
'sym_variables': [('x1', 'red umbrellas'), ('x2', 'blue umbrellas')],
'objective_function': '3*x1 + 5*x2',
'constraints': [
    'x1 + x2 <= 100',
    'x1 >= 10',
    'x2 >= 4*x1'
]
}
```

## 3: Translate the symbolic representation into Gurobi code in Python
```python
import gurobi

def solve_umbrella_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="red_umbrellas", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="blue_umbrellas", lb=0, ub=gurobi.GRB.INFINITY)

    # Objective function: maximize 3*x1 + 5*x2
    model.setObjective(3*x1 + 5*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 100, name="total_umbrellas")
    model.addConstr(x1 >= 10, name="min_red_umbrellas")
    model.addConstr(x2 >= 4*x1, name="blue_vs_red")

    # Update model
    model.update()

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: red umbrellas = {x1.varValue}, blue umbrellas = {x2.varValue}")
    else:
        print("No optimal solution found")

solve_umbrella_problem()
```