To solve this problem, we first need to convert the natural language description into a symbolic representation. Let's denote the number of pizzas as $x_1$ and the number of donuts as $x_2$. 

The objective function is to minimize costs. Since each pizza costs $4 and each donut costs $2, the total cost can be represented as $4x_1 + 2x_2$. This will be our objective function.

Now, let's consider the constraints:

1. The actor wants to eat a minimum of 3000 calories per day.
   - Each pizza contains 300 calories, and each donut contains 200 calories. 
   - Therefore, the total calorie intake from $x_1$ pizzas and $x_2$ donuts is $300x_1 + 200x_2$ calories.
   - The constraint for minimum calorie intake can be represented as $300x_1 + 200x_2 \geq 3000$.

2. The actor wants to eat at least 200 grams of fat per day.
   - Each pizza contains 10 grams of fat, and each donut contains 7 grams of fat.
   - Therefore, the total fat intake from $x_1$ pizzas and $x_2$ donuts is $10x_1 + 7x_2$ grams.
   - The constraint for minimum fat intake can be represented as $10x_1 + 7x_2 \geq 200$.

Additionally, since the actor cannot eat a negative number of pizzas or donuts, we have non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$.

Now, let's put this into the required symbolic representation format:

```json
{
    'sym_variables': [('x1', 'number of pizzas'), ('x2', 'number of donuts')],
    'objective_function': '4*x1 + 2*x2',
    'constraints': ['300*x1 + 200*x2 >= 3000', '10*x1 + 7*x2 >= 200', 'x1 >= 0', 'x2 >= 0']
}
```

Next, we'll write the Gurobi code to solve this linear programming problem:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="pizzas")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="donuts")

# Set objective function
m.setObjective(4*x1 + 2*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(300*x1 + 200*x2 >= 3000, "calorie_constraint")
m.addConstr(10*x1 + 7*x2 >= 200, "fat_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of pizzas: {x1.x}")
    print(f"Number of donuts: {x2.x}")
    print(f"Total cost: ${4*x1.x + 2*x2.x:.2f}")
else:
    print("No optimal solution found")
```