## Step 1: Define the symbolic representation of the problem
Let's denote the number of egg sandwiches as $x_1$ and the number of ham sandwiches as $x_2$. The objective is to maximize profit, which is $3.5x_1 + 5x_2$. The constraints are based on the availability of eggs and ham. Each egg sandwich requires 5 eggs, and each ham sandwich requires 1 egg, with a total of 50 eggs available. This gives us the constraint $5x_1 + x_2 \leq 50$. For ham, each egg sandwich requires 2 slices, and each ham sandwich requires 4 slices, with a total of 60 slices available, leading to the constraint $2x_1 + 4x_2 \leq 60$. Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of sandwiches cannot be negative.

## 2: Express the problem in the required symbolic format
The symbolic variables are:
- $x_1$ for the number of egg sandwiches
- $x_2$ for the number of ham sandwiches

The objective function to maximize is: $3.5x_1 + 5x_2$

The constraints are:
- $5x_1 + x_2 \leq 50$ (egg constraint)
- $2x_1 + 4x_2 \leq 60$ (ham constraint)
- $x_1 \geq 0$ (non-negativity constraint for egg sandwiches)
- $x_2 \geq 0$ (non-negativity constraint for ham sandwiches)

In the required format:
```json
{
'sym_variables': [('x1', 'egg sandwiches'), ('x2', 'ham sandwiches')],
'objective_function': '3.5*x1 + 5*x2',
'constraints': [
    '5*x1 + x2 <= 50',
    '2*x1 + 4*x2 <= 60',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 3: Convert the problem into Gurobi code
To solve this linear programming problem using Gurobi, we will use the Gurobi Python API.

```python
import gurobi

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

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

    # Set the objective function
    model.setObjective(3.5 * x1 + 5 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5 * x1 + x2 <= 50, name="egg_constraint")
    model.addConstr(2 * x1 + 4 * x2 <= 60, name="ham_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of egg sandwiches: {x1.varValue}")
        print(f"Number of ham sandwiches: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```