## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the units of chicken
- $x_2$ represents the units of beef

## Step 2: Formulate the objective function
The objective is to minimize the total cost of the diet. Given that chicken costs $3.4 per unit and beef costs $7.5 per unit, the objective function can be written as:
\[ \text{Minimize:} \quad 3.4x_1 + 7.5x_2 \]

## 3: Define the constraints
The diet must contain a minimum of 100 units of proteins and 60 units of fat. One unit of chicken has 10 units of proteins and 6 units of fat, and one unit of beef has 30 units of proteins and 40 units of fat. Therefore, the constraints can be written as:
\[ 10x_1 + 30x_2 \geq 100 \] (protein constraint)
\[ 6x_1 + 40x_2 \geq 60 \] (fat constraint)
Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the units of chicken and beef cannot be negative.

## 4: Symbolic representation of the problem
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'units of chicken'), ('x2', 'units of beef')],
    'objective_function': '3.4*x1 + 7.5*x2',
    'constraints': [
        '10*x1 + 30*x2 >= 100',
        '6*x1 + 40*x2 >= 60',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code
Now, let's write the Gurobi code in Python to solve this linear programming problem:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="chicken", lb=0)
    x2 = model.addVar(name="beef", lb=0)

    # Objective function: minimize cost
    model.setObjective(3.4 * x1 + 7.5 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 * x1 + 30 * x2 >= 100, name="protein_requirement")
    model.addConstr(6 * x1 + 40 * x2 >= 60, name="fat_requirement")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal cost: ", model.objVal)
        print("Units of chicken: ", x1.varValue)
        print("Units of beef: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_diet_problem()
```