## Step 1: Define the symbolic representation of the problem
The actor needs to eat a minimum of 3000 calories per day and at least 200 grams of fat per day. Each pizza costs $4 and contains 300 calories and 10 grams of fat. Each donut costs $2 and contains 200 calories and 7 grams of fat. Let's denote:
- $x_1$ as the number of pizzas
- $x_2$ as the number of donuts

## Step 2: Formulate the objective function
The objective is to minimize the total cost. The cost of pizzas is $4x_1$ and the cost of donuts is $2x_2$. Therefore, the objective function is:
\[ \text{Minimize:} \quad 4x_1 + 2x_2 \]

## 3: Define the constraints
1. The actor needs to eat a minimum of 3000 calories per day. Since each pizza contains 300 calories and each donut contains 200 calories, we have:
\[ 300x_1 + 200x_2 \geq 3000 \]
2. The actor needs to eat at least 200 grams of fat per day. Since each pizza contains 10 grams of fat and each donut contains 7 grams of fat, we have:
\[ 10x_1 + 7x_2 \geq 200 \]
3. The number of pizzas and donuts cannot be negative:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## 4: Symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'pizzas'), ('x2', 'donuts')],
    'objective_function': '4*x1 + 2*x2',
    'constraints': [
        '300*x1 + 200*x2 >= 3000',
        '10*x1 + 7*x2 >= 200',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code in Python
```python
import gurobipy as gp

def solve_actor_diet_problem():
    # Create a new model
    model = gp.Model("ActorDiet")

    # Define variables
    x1 = model.addVar(name="pizzas", lb=0, vtype=gp.GRB.CONTINUOUS)
    x2 = model.addVar(name="donuts", lb=0, vtype=gp.GRB.CONTINUOUS)

    # Objective function: minimize cost
    model.setObjective(4*x1 + 2*x2, gp.GRB.MINIMIZE)

    # Constraints
    model.addConstr(300*x1 + 200*x2 >= 3000, name="calories")
    model.addConstr(10*x1 + 7*x2 >= 200, name="fat")

    # Solve the model
    model.optimize()

    # Print solution
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Minimum cost: {model.objVal}")
    else:
        print("No optimal solution found")

solve_actor_diet_problem()
```