## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the tons of cocoa beans produced per day.
- $x_2$ represents the tons of coffee beans produced per day.

## Step 2: Formulate the objective function
The profit per ton of cocoa beans is $500, and the profit per ton of coffee beans is $750. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 500x_1 + 750x_2 \]

## 3: Define the constraints
1. Production capacity constraint: The factory has a production capacity of 15 tons per day for both cocoa and coffee beans combined.
\[ x_1 + x_2 \leq 15 \]
2. Roasting machine availability constraint: Each ton of coffee and cocoa beans requires 15 hours of roasting, and the machine is available for at most 1000 hours.
\[ 15x_1 + 15x_2 \leq 1000 \]
Simplifying, we get:
\[ x_1 + x_2 \leq \frac{1000}{15} \]
\[ x_1 + x_2 \leq 66.67 \]
However, since the production capacity is 15 tons per day, this constraint is less restrictive than the production capacity constraint and can be ignored.

3. Minimum production requirements:
\[ x_1 \geq 3 \] (minimum of 3 tons of cocoa beans)
\[ x_2 \geq 5 \] (minimum of 5 tons of coffee beans)

## 4: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'tons of cocoa beans'), ('x2', 'tons of coffee beans')],
'objective_function': '500*x1 + 750*x2',
'constraints': [
'x1 + x2 <= 15',
'x1 >= 3',
'x2 >= 5'
]
}
```

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

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

    # Define the variables
    x1 = model.addVar(lb=3, name="cocoa_beans")  # Minimum 3 tons of cocoa beans
    x2 = model.addVar(lb=5, name="coffee_beans")  # Minimum 5 tons of coffee beans

    # Objective function: Maximize 500*x1 + 750*x2
    model.setObjective(500*x1 + 750*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 15, name="production_capacity")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_optimization_problem()
```